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If you are simply drilling a hole through the board, running the center conductor through the hole, and soldering it to the top-layer copper, then simply placing an Internal port at the feed point should be sufficient. Going to a full 3D EM solver like HFSS would give you the "real" solution, but for what Momentum can do (2.5D), this approach will give you a reasonable approximation.
For 3D EM structures, yes, HFSS is better than Momentum. For a simple patch antenna, Momentum will be more than sufficient to model that structure. You don't really need to model the fields around the launch, so going to a tool like HFSS would be overkill. Using an internal port, like you have shown, will give you good simulation results (assuming your settings are correct.... edge mesh, metal thickness, etc.) I use ADS Momentum for the vast majority of my EM simulation needs, since it's all planar-based.
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