CLR SQL vs T-SQL for queries
First off, just to be clear: SQLCLR / .NET / C# / VB.NET cannot query the database. Only T-SQL can query SQL Server. So in order for SQLCLR code to get data or interact with SQL Server in any way, it must establish a SqlConnection, like any other .NET app, and submit T-SQL, or execute a Stored Procedure.

Yes, you can call a SQLCLR (whether it is C# or VB.NET does not matter) Stored Procedure, or Scalar Function, or Table-Valued Function (TVF), etc from T-SQL. In fact, that is the only way you can call SQLCLR objects. Classes representing the SQLCLR objects, defined in Assemblies, need to have T-SQL wrapper objects defined that point to those classes so that they can be invoked.

Sending complex objects into SQLCLR objects can be accomplished, but unfortunately not via Table Valued Parameters (TVPs). However, you can either create a local temporary table in T-SQL, populate it, and select from it in the SQLCLR object, OR you can package up the complex data in XML and pass that in as a parameter to the SQLCLR object that will traverse it via an XmlReader.

For getting the data back efficiently, you can either:


Issue INSERT statements from the SQLCLR Stored Procedure
Create a T-SQL Stored Procedure that accepts a TVP and call that from the SQLCLR object
return a Result Set from the SQLCLR object that is used in an INSERT statement, as as INSERT INTO ... EXEC for a SQLCLR Stored Procedure, or INSERT INTO ... SELECT for a SQLCLR TVF.


As far as loading you DAL libraries goes, that could work, but there could also be complications. It all depends on what you libraries are doing and what Framework libraries are being referenced. Only a small subset of the .NET Framework libraries are supported in SQL Server's CLR host, so if your libraries reference other libraries that are not "approved", then you will need to load those libraries manually, along with any of their dependent libraries (if there are any). The complicating factors here are that loading unsupported .NET Framework libraries requires that they be set to UNSAFE, which in turn requires that the Database be set to TRUSTWORTHY ON. The other complication is that loading the .NET Framework library might not even be possible in the first place since the CLR host inside of SQL Server only allows pure-MSIL Assemblies, and so you cannot load mixed-mode Assemblies. Some .NET Framework libraries are currently mixed-mode and won't load. Others are currently "pure" and will load, but there is no guarantee that those will not ever be changed into a mixed-mode Assembly in a future .NET Framework update. If/when that happens (and it has happened, such as with System.ServiceModel), then you will need to re-code you Assembly. So it's best to stick with the supported Framework libraries as those are guaranteed to continue working through future upgrades.

Keep in mind that App Domains are per Database, per Owner (of the Assembly). This means that, in terms of any particular SQLCLR object, all sessions / SPIDs will be calling the same code and sharing the same memory. This is why the methods need to be declared as static. And this is why attempting to use non-readonly static class variables requires the Assembly to be marked as UNSAFE: because the value of such a variable can be overwritten by another session / SPID (case in point: SQLCLR assembly throws error when multiple queries run simultaneously).

With respect to this statement in the Question:


  as for performance I assume it would be better or at least not noticeable in comparison.


I wouldn't assume anything here. There are a lot of factors that influence performance in either direction:


some datatypes transfer back-and-forth between SQL Server memory and .NET AppDomain memory faster than others
how you code your algorithms in C# (I recently wrote a simple function for someone who had already gotten another suggestion that used LINQ -- the LINQ version took 375 - 400 ms to do the same thing that my version, with more lines, took only 2 - 9 ms to complete, a 41x - 200x difference!)
how much data you have (sometimes T-SQL is faster with smaller values -- usually strings -- where SQLCLR might be faster with longer values)
are you following best practices? If you are coding a deterministic SQLCLR scalar function and don't mark it as IsDeterministic=true, then you can't get the benefit of it being able to participate in a parallel plan (something T-SQL UDFs can't do).
etc


Hence: don't assume; test!

If you are looking to learn more about working with SQLCLR, you might want to check out a series that I am writing on this topic on SQL Server Central: Stairway to SQLCLR (free registration is required to access their content). There are several articles and more coming, and plenty of examples to illustrate various features, security, etc.



Regarding Azure SQL Database: please note that while support for SQLCLR (SAFE Assemblies only) was added in late 2014, it was recently (and supposedly temporarily) removed. Customers were emailed on April 8th, 2016 of the feature being removed on April 15th, 2016. The most official notice I could find was this thread on reddit:

Customer:


  Is support for CLR Assemblies in Azure SQL going to end any time soon?
  I ask this because I received an email this morning (supposedly) from Microsoft stating that this feature will no longer be supported after April 15th (!!!).


Jan, a PM in the Azure SQL DB team working on performance and Elastic Pools:


  The email you received is indeed real. As stated in the mail, we determined that there is a security risk with user-defined SQL CLR in SQL Database. There have been no known exploits to date. In an effort to help protect the security of our customers, we have proactively suspended the use of user-defined SQL CLR in Azure SQL Database. This means that user-defined SQL CLR will no longer work. We will update you within six month with a timeline for bringing back SQL CLR.


and Tommy, a PM in the Azure SQL DB Security team:


  This issue only applies to the Azure SQL Database service, not SQL Server on-prem or IaaS.