most likely not... your best bet is to leave your solara stock and attempt to get another vehicle to race...

Some likely cheap 12 second ideas include. (with toyota first since this is a toyota forum)

3rd generation turbo supra (lots of help to be found on this board)
1985-1987 Toyota Corrola GT-S
AW11 mr2 (first gen)
Third gen RX-7
Honda CRX or Honda Civic Hatchback (swapping it)
Nissan 240sx's of all years..

All of these provide a decent base for power. For around 8000 dollars, most of these cars would run siginifigantly faster than even 15 K dropped into your solara...