Wake reinforced? I think it's possible given the available fleet units of the US Navy at that time. However, it would have been a very risky proposition because the Japanese held the initiative and the US would be reacting to a Japanese move. It's an iffy thing. If both navies had their fleet in place, a battle similar to Midway could've occured. But predicting the outcome is beyond me. At Midway, it was an iffy thing.
But the long term bottom line would still be this. The US would still win the Pacific War because it had a better naval doctrine, (better use of subs, etc). Another thing, if we go by attrition, the Japanese would eventually lose because the US had a better system in place to replace what it lost.
As to Wake Island itself, the size of the island meant that it couldn't support a large garrison. It would have to depend on ships for better protection.
Tying fleet units to a specific spot at that time of the war would mean that Japanese naval units would be free to move elsewhere in other areas.