One thing to note: We'd have to have roster space for all of those players. You're not allowed to have more than 15 guys on your roster at any time during the season, even if your immediate plan is to cut them.
Yeah, not sure if you can make it work. You would have to cut Wilcox and Collins to get down to 11, then trade one guy for 5. That puts you at 15, then you would have to waive 4 from the Bulls trade, just so you could trade one more guy (Pierce) for 5 more from Houston.
A more resonable idea would be trade Pierce to the Warriors for Jefferson, Rush, and Barnes. You would then have to waive Jefferson and Rush and eat the remaining 2 years on the deals, plus waive Wilcox and Collins to get down to 11 and pull off the KG trade.