From what I have seen, if some of the free agents the Giants lost do well, the Giants may get a 4th round comp pick.
That all goes away if the Giants sign another player for more than the veteran minimum or that boosted minimum.
So, if the Giants are going to make any significant signings it will be after some day (not sure the exact date) in the beginning of May when any free agents signed after that date don't impact the comp pick formula