Yes, you can use a mobile phone on the receiving (and also on transmitting) side.

But, there are a number of buts here.

Mobile phones are normally very porly documented. The manufacturer did not develop the phone with the intention of supplying end users with the required documentation to implement good computer support. They may have limited themselves to just work with Microsoft in the Windows support.

This is a (non-complete) list of things to think about:
- you will need to find some official documentation or other projects with documentation, that tells you how to communicate with the phone electrically. What pin numbers. What signal levels. Any special needs for powering the phone (remember that it must be powered 24x7).
- you will need to find some documentation or any project with source or other documentation that shows to you the feasibility and use of all the commands you - at a minimum - requires to get your project working. You may hope for standard GSM documents, but you should never base a project around a mobile phone unless you have proof that you have all documentation needed. Just knowing that the phone is up to the task isn't enough, if you still get stuck on an undocumented feature.
- you might find a RS232 cable, which is fine when communicating with the PC. But with a RS232 cable, you would have to use a MAX232 or similar on the microcontroller side. Or you might be able to find information how you can connect the phone directly to your microcontroller, either in a 3.3V or 5V setup.
- mobile phones are known to hang. You must consider how to automagically restart the phone if that happens. Remember that if you have a PIN code on the SIM card, the phone will expect someone to enter that PIN code again after a restart. Who would do that in the middle of the night, if it happens on the server side? Who would visit the vehicle in case it happens on that side? How would you even know where the vehicle is, if it can't report in the position?
- how would the PC be able to turn on/off the power to the phone, to force a restart?
- how will you find out about any problems with the subscription?
- some phones does not work well (or at all) without a battery.
- some phones does not work well, if constantly charged.
- if you don't have documentation for the commands, how will you understand any error codes the phone may emit?
- the phone can accept a limited number of SMS (maybe 100) before you must erase them. What happens if your PC or application hangs so the phone SMS memory gets full? The SMSc that buffers and sends SMS in the GSM network will only cache a limited number of SMS message to a subscriber number.
- will you have full control of the phone profile, so it neither beeps, vibrates or in any other way disturbs when receiving an SMS?
- what are your chances of upgrading from SMS to MMS, in case you later want the vehicle to send in a photo in case it thinks it has been stolen? Will you have all requierd information about the phone to be able to make this kind of improvement?
- some phones supports use of an external antenna. Will your do that? What happens if it doesn't,and the room has bad reception?

On the net, you can find a huge number of projects started with a mobile phone. Quite a number of projects fails. Quite a large number. Cheap is not always good.