Doubtful - we'd have to cut someone to make room -for- Branch, and then hope that Minnesota would have had paid the same price, instead of offering less since we'd be carrying a surplus of WRs.
That's not even mentioning the potential circus that would've happened if Branch/Moss were on the same team. The Moss distraction would only have metasized at a rate that the Patriots might not have been able to handle.
One other point I wanted to bring up:
The Patriots made the deal essentially because Branch agreed to renegotiate his contract to something more agreeable to the Patriots.
So the contract that Seattle didn't want was amended to a more team-friendly contract the Patriots were willing to give up a fourth round pick for. I'm not sure the Patriots would have agreed to the fourth round pick if Branch hadn't renegotiated his contract to something more Patriots-friendly.