Get the Messages stream in an SSRS RDL Report
Removing what I had previously answered, since it was way off. Based on your comment regarding PRINT statements and getting the rows affected messages...

The rows affected message is something SSMS returns, you would generally not see that with datasets in SSRS that I know of. 

I did some testing with PRINT statements and in SSDT-BI for SQL Server 2012 the statement is ignored and not returned in my case. As well, there are only so many places that you can actually put a tooltip so you might need to expand a bit more on how and where you want to use this information.

With regards to your specific report if you are having issues with a report rendering only 1500 rows there is no real way for us to assist in that unless you share it more about it, or the actual RDL file.