Question Knowing that a motherboard can support a GPU without a external power plug,would the power consumption at the wall increase by 75 watts using such a


yeah, a 180W PSU is probly too weak to support anything. I'd go with at least 250-300W.

power draw at the wall will vary by the PSU's efficiency rating.

so, lets say you have a system that uses 300W, an 80+ PSU (80% efficient) will pull 300/0.8 = 375W from the wall. an 80+ Bronze PSU (82% efficient) will pull 365.85W from the wall. in either case, the excess wattage becomes waste heat.
Yup, agreed with above. Not to mention, the "180W" PSU probably can't supply 15A on the +12V rail (12V x 15A = 180W) There's a sticker on the side of your power supply that shows this info.

What is your actual machine? If the mobo and case accept "standard" ATX PSUs, a replacement isn't very expensive (Corsair CX450 = $20 after MIR) AND then you're not limited to a GPU without external power.