Sounds plausible to me. I have seen slow blow fuzes glow when they are in a circuit that is drawing close to their rated current. It may have been a bad/cheap fuze with a few hundred milliohms resistance as well. Have you tried another 20 AMP fuze? The previous posts cautioning you about oversizing the fuze are correct. If you overload your Inverter, somthing in it may pop instead of the fuze and this might cause damage to what ever your Inverter is powering at the time.
Walt
http://www.safossils.com/mp3car.html
http://www.safossils.com/waltsongs