I am using Linux Ubuntu 11.10 (Oneiric Ocelot) with all extras...
OpenCL allows all graphic cards to be handled in a higher level in a uniform fashion. As all GPU mining software relies on OpenCL, you would need to create your own software to mine on non-OpenCL card. Whereas it is possible, the process would be very complicated and the reward probably wouldn't be worth it (NVIDIA cards aren't good for mining).
So all in all, no, if the graphic card does not support OpenCL, you can't use it to mine.
The 7300's GPU isn't sufficiently software programmable to be used for mining. There's no known way to get it to mine Bitcoins.
Try using CudaMiner since it was written specifically for Nvidia cards and does not require OpenCL.