Not really, part of the doctrine was the Open Door.
Wasn't the Open Door Policy enacted
after the Spanish-American War? My date for it is late 1899, though I could be wrong.
But it was considered at the time tat there could possibly be grounds for an intervention - it is most assuredly not part of the Western Hemisphere, and it can't even be counted as part of the New World if you stretch the definition and include the majority of Oceania within that - the Philippines are in Asia. If not for the resounding success in taking the Philippines in the first place, the US feared they might have overplayed their hands.
As it stands, the US was also intervening in an existing Spanish colony to assist it in maintaining its tepid and fragile independence - they forswore the existing policy of neutrality in a conflict between colonial power and colony until they resolved it on their own terms. That's already pushing the doctrine far enough. There is nothing in the text of the Monroe Doctrine relating to Asia, but it also promises that the US will abstain from intervening in the insular issues of the European nations. Invading the Philippines risked triggering that insular issue button, at the very least. It ended up coming to be nothing, even if war scares with other nations during that time have been noted. (Germany esp)