No. Not all onboard video chipsets can handle 1080p. I'm not sure about the Intel GMAX4500 chipset. If you want to make sure your system can handle 1080p playback, stick with the Intel Core I3/H55 setup that Griffolion suggests, your original NVidia ION setup (they do make Mini-ITX motherboards for desktop solutions - Search "NVidia ION" on Newegg), or the AMD 785G/890GX chipsets.
My personal recommendation would be the 785G AM3 motherboard paired with an Athlon II X2 processor or this Mobo/CPU/GPU combo
as a base. Either will come in between $40 and $60 cheaper than the Core I3/H55 setup.