Will my Sprint phone work?
Yes. It should work most places in town. The east side has no service and far north and south have sketchy service, but in or near town (or out on the water) GSM coverage is great. CDMA coverage isn't as good as the GSM service. Overall, coverage is much better than at my home in NH, which Sprint lists as not having any service at all.
It'll be very expensive, though, as Sprint charges high international roaming rates for calls and texts and even higher for any data use. Sprint does not offer any international roaming packages (like the great one Verizon offers).
Will it have to be modified with a new memory stick or SIM card?
If your phone has a GSM radio (all Sprint iPhones or things sold as "world phones") it doesn't
have to be, but you should get a local SIM in order to save big bucks.
Note that a SIM and a memory card are very different things. Whether you swap out a memory card makes no difference in terms of using the phone on the network since it only affects storage. Changing a SIM will take you off Sprint (preventing roaming charges but also preventing you from making or receiving calls on your US number) and put you on whatever carrier sold you the SIM.
Cheap. A Telcel Amigo SIM costs 149 pesos and comes with 50 pesos of airtime.
Is there a temporary use phone I can buy that is basically a throw away for when I return home?
Sure. There are quite inexpensive ones, but they will be more than simply buying a SIM if that's an option with your phone.
Depending upon your needs, there may be options that are completely free, and you'll certainly want to use them if you can't pop in a SIM. If you have a) a smartphone and b) access to Wifi (which many hotels, rental homes, and local restaurants offer for free), you can make free calls to the US or Canada using the free Magic Jack app (even if you don't have Magic Jack service) as well as a few other options. These will in general not allow people to call you for free and they won't let you use your home number.
If you want to go the SIM route, you
must get the SIM slot unlocked by Sprint before you leave the US. Sprint cannot do this when you're in Mexico, and all Sprint phones come with their SIM slots locked so if you put in a foreign SIM it won't work. You need to call the International Support number +1 (888) 226-7212 and ask them to "unlock my SIM for international use". They have some requirements such as that the account must be in good standing and that you must have had the device for more than 60 days, but they will otherwise do this on request. It can take a couple of days, so don't wait to the last minute (and remember you must be within Sprint's domestic coverage area when they send the unlock code!). Note that any service other than Sprint
cannot do this, no matter what they may claim, and they'll charge you for something Sprint will do for free, so don't bother with them.
Once you get to Cozumel with your phone with its unlocked SIM slot, go to one of a zillion mobile phone shops or Oxxo convenience stores or to the new Telcel Customer Support Center on Juárez and 35 Avenida and ask for a "chip" (pronounced "cheep"). You'll probably also want to add more airtime than 50 pesos and you may want to purchase an inexpensive data plan. I have
a table of data plan prices and parameters translated from Spanish that you can consult if you like.
To add airtime, you can buy a scratch card and type in numbers, go to an Oxxo convenience store or most large grocery stores and have them do it wirelessly, or use the mitelcel.com website or the Mi Telcel app on your phone. To add a data plan you first ensure you have enough airtime credit to cover the cost (I typically get a 7-day 400 MB plan for 99 pesos) then send a text code (listed at the table above) or add it from your computer or the app.
