It will depend on the nameplate ratings of the "300W" PSU. Total PSU wattage means very little. It is all about the +12V rail specs when it comes to gfx cards. Nvidia recommends a 400W min for that card, although a strong 300W PSU using a Molex adapter would probably be OK.
If you don't already have the GTS 450, there are much more powerful gfx cards available that will indeed run on most 300W PSUs. In fact, even modern integrated graphics are more powerful than the GTX 450.