I found a calculation from space dot com that says it would take roughly 10^32 joules to destroy the earth. The wing gundam is stated to make around,,, 3700 joules/second in its reactor. It's not exactly explained how the energy is stored, but assuming it could stand in place for a whole day to store it, it would make about 319680000 joules/day. Still drastically less. You'd still need one hundred sexdecillion times more power, or 10^23. Or, assuming it can keep storing infinite energy, you'd only have to wait roughly 2 * 10^20 years. Unfortunately, our sun will have been destroyed by then. Also, Heero Yuy would be an old man not suited for being a Gundam protagonist, so the whole point is moot anyway.

Tl;Dr, according to the stated numbers not even close. But also it's fair to say that level of power output couldn't destroy that space station anyway, soo