It would be very helpful if it was sorted out before the draft.
Trading after the draft would mean you go a full season without both the player as well as the compensation you receive back for him.
Typically the difference in a draft pick from one year to the next is valued at one round. (IOW a 2018 2nd round pick is of comparable value to a 2017 1st round pick).
If Butler is theoretically worth a 2017 1st, that ups the ante in value of 2018 picks to the point where it makes it difficult for the other team to put together a worthwhile package.
It doesn't make much sense for the Patriots to trade him after the draft. Might as well keep him and get the benefit of his playing in 2017. It also gives the Pats more time to work out an extension.
STEP ONE
On April 23rd (date subject to check) Butler will have signed an offer (which we will match or not) or Butler will sign his RFA for $3.91M.
STEP TWO
If Butler is still patriot property after April 23rd, the team negotiate with any team, permeably before the draft, although the team could negotiate during or even after the draft.
21 April is the last day that other teams can give him offers. After the 21st it's NE or nothing.
The next relevant deadline is 15 June. If he doesn't sign it by 15 June NE can but does not have to reduce the tender from $3.9 mil to 110% of previous salary, so around $700K (I don't know the exact number).
The next relevant deadline is week 10 of the regular season. If he hasn't signed it by then he does not pick up a year of service and will remain a RFA the next offseason.
So once 21 April passes the only reason for him not to sign it is if he still thinks he can get an extension from NE.
But in no event can he be made to sign it or is it considered automatically signed. He's not under contract until he actually signs it, whenever that is.
If the patriots sign or match a long-term contract with Butler, there will be no need to acquire more corners, except for camp fodder. Gilmore, Butler, Rowe, Jones, Jones and Coleman are quite sufficient.
Of course, when someone says a position is still a need with regard to depth, it is a bit difficult to disagree with. After all, almost every player is upgradable.
So, for me, corner is not a need unless Butler goes. I suppose the easiest way to look at the situation is to think that we are fine with Butler or whoever we draft any compensation.