if they did, they possibly could. but your average cellphone works off local cellphone towers with a very limited range, beamed across the surface og the earth - not into space. There is a system of satellite cellphones, called Iridium (I think), but since they are aimed at the ground, you'd probably still find it hard to get a signal.

Cell phones don't work of satellites, but off land-based base-stations in tall buildings and towers. The whole point about cell phones is they are based on cells - relatively small areas that have a limited number of users in each cell. The cells vary in size, so in empty country they many be many miles across, while in the city they may only be a few hundred yards across - or even less in vary busy areas. While you can move seamlessly from one cell to another, the assumption is that you would not do so very often, So if you were in space you would need a base station somewhere near you and moving in the same orbit. If the base station were not in the same orbit, you would need a huge number to ensure that one was always nearby,

See Wiki: A satellite telephone, satellite phone, or satphone is a type of mobile phone that connects to orbiting satellites instead of terrestrial cell sites. Depending on the architecture of a particular system, coverage may include the entire Earth, or only specific regions. Satellite phone (Inmarsat)The mobile equipment, also known as a terminal, varies widely. Early satellite phone handsets had a size and weight comparable to that of a late 1980s or early 1990s mobile phone, but usually with a large retractable antenna. More recent satellite phones are similar in size to a regular mobile phone while some prototype satellite phones have no distinguishable difference from an ordinary smartphone[1][2]. Satphones are popular on expeditions into remote areas where terrestrial cellular service is unavailable . . If you had a clear line to a satellite, it should work.

It is rather unlikely that the cellular network model will ever be used in space other than fx locally on the moon or on a space station. The main benefit of a cellular network is that each repeater have a very limited range. That enables us to reuse its frequencies in other repeaters that are distant enough to avoid the two signals (on the same frequency) to be confused. This small size of the cells is also used in network administration because even at light speed there is a delay between phone and repeater, and for parts of the protocols used phones MUST be effectively synchronized with each other (eg: the repeater send an administrative message to all phones in its range "If the signal from your currently assigned repeater is getting bad you can request assignment to this repeater by sending your ID in the slot coming up in .01 seconds". Cellphones respond, but those on the periphery of the cell respond slower because the signal needs more time getting there and back. That forces the slot to be wider to make room for the possible response delays. and the wider the response slots, the less time you have left over to actually transmit signal in. Distances in space however are BIG, and mostly very empty. It is totally unrealistic to put in orbit a repeater for say every 50 cubic miles of space, and almost none of them would be in use at any given time. Instead I expect we will use directional beams (empty space make it fairly easy to create coherent radio beams that can transmit over huge distances.) regards JakobA PS: Iridium was a stopgap solution, created by Motorola, mainly for advertising how hi-tec and ahead of the pack they were. Full cellular coverage require a HUGE investment and before everyone had jumped on the bandwagon and made that investment it was a lot cheaper to put satellites in orbit and use them as repeaters for the rather small nr of phones they were able to handle. Those were not normal cellphones, but about as big as the old walkie talkies and transmissions were mainly directional.