Ota antenna on cable coax with internet on line
No, you will need to isolate the two systems from each other.  They cannot exist on the same coax.

Unplug lines one by one from the splitter until you locate the modem.  That line must be connected to the incoming cable from the cable company.  You may need an inexpensive F-Type Coaxial Cable Connector from the big box store to join the two cables. 

Important note: both systems do need to be grounded.  Without more information on your current system it's hard to advise.  The ground in this case has multiple functions, but is primarily grounding static charge, providing ground reference, and possibly preventing a surge from damaging equipment.

Once the modem is isolated and connected directly to the incoming cable, then you can use the rest of the existing distribution system to distribute your OTA TV to the TV's.