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Yes it can - if you have the right equipment.
You can buy devices which will send IR signals over your coax cable using DC signals without interfereing with your TV signals. IR is received by special IR receivers and then converted to DC electrical signals for transmission over the coax cable. On the remote end, the electrical signal is sent to your A/V devices using an IR transmitter.
One important thing to note is you must have the proper splitters in your cable system in your house for this to work. Normal splitters do not pass on DC signals. You need to us special splitters which can pass on DC signals. Then the IR data can go to all the TVs in your house.
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Home Automation FAQ : 
My modulator has Left & Right Audio Inputs - can it transmit in stereo?