Can any coax two-way splitter also be used to combine two sources to one line?

I have a splitter that looks similar to this guy. But the Radio Shack page lists theirs as a hybrid capable of working in either direction: as a splitter or as a combiner.

So, I already have a generic-looking one lying around. And I have two coax sources (satellite and over-the-air antenna). But only one coax input on my TV.

I’d like to plug both my sources into the two port end of my generic splitter and my TV to the one port end.

And my hope would be that I could toggle between the two sources on my TV just by selecting either CATV or AIR as the source.

Is my generic splitter okay? Or should I try to get this Radio Shack hybrid model?
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Yes, I know about A-B switches. But that’s not on the table for this discussion.