Yes, we gave up three picks. However, one was quid pro quo in exchange for Harvin himself--a pick for a player. Only the third and seventh were extra picks that could be counted as "lost" in that trade.
Unless you work for the Seahawks, you cannot definitively state that Tate is gone because of Harvin's salary. Someone is gone as a result, but it may or may not be Tate.
OK, now that I'm back on a computer instead of a phone, I'll add this:
I understand where you're coming from. On the surface it makes sense that we gained an expensive WR and therefore lost another WR because we didn't have enough money to pay him. But cap management doesn't work that way. They aren't just looking at each player on a micro level--they have to look at the overall team composition in terms of age, depth, money, etc. There also is the fact that some players will end up leaving for any number of reasons: money, playing time, scheme fit, and so forth.
There is simply no way to state that player A automatically means we have lost or will lose player B based on their playing position.