If you did that you'd definitely never be accused of front-running. Giants play in a pretty tough division (especially so if Washington is relevant). But yeah as far as the draft goes, if you don't have a top 10 pick (or top 3 if you're going for QB) then it's really nothing to get too excited about and not worth the hype it generates.
One, I grew up a Giants fan; that's how I got into the Patriots, via Belichick.
Two, not sure I follow the latter part. I can't recall once ever being "excited" about draft picks. It's one step in the process and just as many star picks flame out as flame on. Honestly, I like Belichick's approach of staying clear of the top ten or so. I just don't think the risk is worth it.