No, arbitration isn't killing them. They can spend a little money when needed. They had a payroll close to $70M the year after they won the WS. They've been dumping talent for prospects lately and trading away salary because they know they need to rebuild more often than most teams because they can't afford to keep a roster at that level. I think they'll keep him as long as they can, and will only trade him if their requests for the moon in return are met. And, I don't see that happening because I think Miggy will test the market.
It could go the other way, but I'll be shocked if they accept less than their demands. Just like it will be very surprising if he elects to sign an extension with a trading team. All the factors point to free-agency.
I will say this, if he doesn't make it to the market, then the Sox should spare no expense to get him on the roster and extended long-term.