First...do NOT buy the stock until you have the approved Form 1 in hand. If you simply must buy it because fo a great deal or something, store it somewhere away from the pistol until the paperwork comes back. Possession of both items in the same place (safe, gun room, etc.) can be construed as 'constructive possession' by the ATF. Are you likely to get busted for that? Probably not, but I tend not to create jeopardy where there is no need.
As to the stock, if you remove the round plug in the back of the receiver, virtually any AR type stock can be used. ACE stocks offers folding versions specifically for the SIG 556, but there are other adapters that will work as well. Nordic Components offers a collapsible wire stock similar to those on the old M3 greaseguns that I have on a 10/22 and have considered using on the 556 since it requires no buffer tube. If you google 'SIG 556P SBR', you will get a number of hits on various boards that will offer options for your build. Getting the plug out of the receiver varies in difficulty from easy to ^&%$#*@ hard depending on how much loctite the guy building your pistol decided to use that day. The board discussions dwell on this a bit.
Another option is to purchase the entire lower from SIG or a secondary market source. It will run a bit more money, but you can easily swap back to pistol configuration (a legal conversion, should you wonder) without much hassle. That was the route I took. Since the upper on the SIG is the serialized part unlike the AR, buying another lower is just like buying a scope or grip. There is one currently for sale on
www.sturmgewehr.com.
And I forgot that you could also buy just the folding stock that SIG offered on the original pistols. It is an AR pattern stock, but manufactured (or contracted out) and marked by SIG for the rifles. They were scarce and expensive for a while until the "Classic" model was introduced using the old 551 profile. I actually have one of the SIG stock adapters floating around the garage somewhere.
Hope this helps.