More than likely. There should also be a can/bottle of tire sealant either on or with the pump.
The sure way to know whether your car came with a spare or just a sealant kit from the factory is to look at the tire and loading label on the driver's door or driver's doorjamb.
If your label is like this one, and says "None" in the spare category, than a sealant kit is correct, but that doesn't mean you can't add a spare.
If you want to add a spare, call your local salvage yard, they'll usually sell the whole kit for about $100 or so (vs $200-300 for the dealership). You could also source a bottle jack or scissor jack and a 4-way lug wrench from a parts store and get a full size steel wheel with a cheap tire from somewhere like Discount Tire for a budget full-sized spare (though it may make your trunk carpet not fit correctly).
I ordered my 2011 v6 in February 2010 with every option available except the glass roof. No spare tire was offered, just the pump and goo . A year latter I ordered a new spare tire wheel and jack made for the 2010 GT. Ended up paying almost $500 for it . Ford now has a spare tire option you can buy for a lot less than the $500 I paid for mine .