Without knowing what the cooler is rated for, it'd be impossible to say for sure. I'd recommend picking up some sorta aftermarket fan if one doesn't come with the X2 you ordered.
That board is an AM2 board, and from the looks of it a Dell at that. The chip you want to put in is an AM3+. The board is listed as compatible with AMD Athlon 64 X2 Dual-Core, Athlon 64, Sempron.
Without knowing what the cooler is rated for, it'd be impossible to say for sure. I'd recommend picking up some sorta aftermarket fan if one doesn't come with the X2 you ordered.