Depending if it's the low profile desktop or the full size desktop it may or may not.
Unless it has the low profile bracket you must use in the full size tower, if you do have the low profile bracket then both should work. The only issue you may ever run into would be possible lag from the graphics card due to the system only have a 200w PSU. I pulled up the specs from the HP website and it states the USDT (Ultra-Slim Desktop), SFF (Small Form Factor), and the CMT (Convertible Mini-Tower) all support the NVS 280 and 285 so I'd imagine it'd support the NVS300. Just verify that your motherboard has a PCI Express 1x slot. I've seen PC's with 230w PSU's run a GT430 without any hiccups so I wouldn't worry about power.
Link to more details -http://h18000.www1.hp.com/products/quickspecs/12543_na/12543_na.HTML