A full 1750W is 145 amps of 12V draw, you'll need to run at least 4 gauge and preferably 2 gauge cable for it but otherwise I don't see why not.
Now if you're just going to run a microwave as your biggest draw then you can match the cable to your need, if 600W is needed now you're talking 50A on the 12V side. You can get away with 10ga there but I'd recommend no smaller than 8ga.
I've got a 1250W inverter and ran 4ga cable with soldered on lugs. She purrs like a kitten.