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You can play e.g.

1. e3 e5 2. e4 whatever

And you effectively have a king's pawn opening with colours reversed

Can black refuse this 'color switch'? It seems like he can, for a while, by mimicking moves. 1. e3 e6 for example.

Does this strategy necessarily leads to provably losing position?

Provably there's little that can be said about chess at large when it comes from opening to endgame. Heuristically speaking though matching moves against even a beginner is a very bad strategy for play, as a recent speedrun being done by GM Aman Hambleton on youtube has been showing.

[1] https://www.youtube.com/watch?v=uUfF6l4A6Ks

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