Yes you can grow mounted orchids just fine in an apartment if you have the window space to provide them. Here's a pic of mine

I have mini orchids and seedlings mounted as well as blooming-sized mature orchids mounted (and others as well). Hope the picture gives you some hints of what you can do.
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Ross
http://orchids-ross.blogspot.com/
I don't do most Dendros or large, "floofy orchids". For me it's minis (like Angraecoides), Paphs, and others that crept in somewhere along the line. See my orchid list for complete collection (usually not current.)