Thanks for all the comments.
I guess my broader question is whether it's worthwhile to pay for one of the "Pan International" SIM cards, which appear to carry a considerable premium for convenience, or whether I'd be better off just buying 1 or 2 SIM cards (depending on country) and paying the roaming (particularly data roaming) rates.
Assuming that I'm not making a ton of lengthy phone calls, it seems like it might be best to just pick up a SIM card upon landing and find something with relatively low roaming costs.