First yes it's possible to do your 'proof of concept' test on a client PC.
The following guide shows how to set this up step by step:-
www.vodafone.co.nz/mobiles/wap_guides/ ericsson_t68_handset_guide.pdf
You'll probably need to change the APN to suit your carrier though.
Once connected you can use the GPRS connection just like any other interbet connection.
The T68i does not have an embeddded user accessible TCP stack, so you'lld need to implement PPP and TCP/IP on your 8051 if you need to use the T68i.
There are lots of GSM modem that have a built in TCP stack though, one example is the Sony Ericsson GT47:-
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