Yes, it will work. However, if you are willing to put in an additional $13, you can get this card:
Newegg.com - ASUS EAH4550/DI/512MD3 LP Radeon HD 4550 512MB 64-bit GDDR3 PCI Express 2.0 x16 HDCP Ready Low Profile Ready Video Card - Desktop Graphics / Video Cards
Still not cutting edge, but it packs more punch than that 3450 and will still work in your computer (PCI-E x16, 300W PSU).