SQL Server 2000 Replication, Performance, and Query Priorities
Note that You are arguing for an UNSUPPORTED version of sql server.

Apart from that read below :


  but the DBAs are telling us that Replication in SQL Server 2000 doesn't work and/or that it has a severe performance impact on the source server.


This is completely False. Why would T-Rep not work in sql 2000 ? Why would it have a severe performance impact on source server ?

The only impact that I can see is 


During the initial snapshot generation as it locks the table while the snapshot is generated and if the table is huge then it will lock it for longer durations. Imagine this causing blocking or possibly timeouts.
when you are replicating the entire database (not only required set of tables/articles) and when you want to reinitialize the replicaiton - meaning new snapshot !
When the n/w bandwithd is not good or there are n/w related issues. 


Above holds true even today for sql server 2012 or 2014.

Note that T-Rep on sql 2005 and up has improved a lot, but the argument your DBA has made is baseless. We even has some legacy applications running on sql 2000 and we use replication heavily and is stable in sql 2000 - no issues at all.


  if it is true/not true that queries from Stored Procedures or queries called from a Linked Servers will take precedence over other queries (e.g. dynamic queries from a connecting application).


Again completely baseless or you might have misunderstood it. Stored procedures can have their plan complied and stored in procedure cache and the plan can be reused.

I don't think you can have priority of the kind you have mentioned.