Ben, the simple answer is NO.
A stored procedure is a compiled SQL statement where it has been checked for syntax errors, and depending on the back end, it might find the least cost (fastest) way to run. This only takes a very short time, so you won't notice any speed improvements no matter how large the db table is.
However, if you are doing something complex that you can NOT accomplish in 1 complicated SQL statement, (i.e. if you have to have multiple FINDs, then a SP can be much faster to run (and perhaps, easier to write / understand / document).
I probably have 10-20 that I use in my application, but all are multiple nested queries or they are queries with temp tables, or they are dynamic sql statements where the where clause is dynamically created (where both sides of the "=" statement can dynamically change).
Bruce
p.s. You didn't ask about the network traffic issue. If I can have the server do more of the heavy lifting and instead of returning 1000s of row to have Aware only use a few of them, then a SP might be the way to go. But that's another topic.