if you have redundant supervisors and you are using the GB ports of the standby supervisor, then YES, there will be STP re-convergence if you pull either of the sups out to swap.
the amount of time STP requires to converge is dependent on the size of the L2 network, STP configuration & STP version. i don't think we'll be able to tell you exactly how long STP needs to converge in your network.
not knowing your topology or STP configuration, i think i would be safe to say that STP convergence should not take more than 1-2 minutes. (this could be off if your L2 network is extremely big or your STP configuration is non-optimal)