Yes, that's normal in Logicâ€”selecting/arming the Track puts it in "ready to play" mode.
>> Is there a way to not have to have the MIDI track armed for recording and still hear my MIDI keyboard?
We-ell.. Yes, but you'd have to cable it in the MIDI Environment (see screenshot), which can get a bit hairyâ€”unless you really need that functionality I probably wouldn't bother, but if you want to try it you can set it up as in the screenshot. Since it would make that instrument always live/playable even with other tracks selected, the Cable Switcher object shown would let you turn it on & off.
Of course if the MIDI keyboard has its own internal sounds you could simply play one of them (Local On), but I assume you mean a virtual instrument sound..