Bill must have - or should have - drafted Edelman to be his Wildcat.
So it seems to me that, in order to perform his Wildcat duties, Edelman needs to show that he deserves to take snaps with the Regular Offense by becoming at least an adequate RB and/or WR.
I don't believe that he is in direct competition with Lewis, who is quite clearly the #4 WR. It's the people vying for the #5 & 6 spots who are his competition: Aiken, Slater, Ventrone, Nunn & Ortiz. Tate is likely headed to the PUP list, and that will give Edelman more time to showcase his return abilities, such as they are.
Also keep in mind now that Paris Lenon has signed, the need for a ST "maven" has been reduced by one; therefore, the aforementioned WRs, plus DBs Spann, Tank, McGowan & Richardson, plus LBs Alexander, TBC & Vinnie C might all have to prove - by a little more than before - that they can play a position, too. And whosoever amoung them can better prove that, will have the upper hand for a permanent place on the 53.
In the end, I would have drafted RB Rashad Jennings, or OL Gerald Cadogan, or WR Kevin Ogletree, or TE Dan Gronkowski, or DEs Michael Bennett, Pannel Egboh or Zach Potter, or LBs Lee Robinson or Nick Reed instead.