There are two major factors to consider in this scenario...
1) A TV antenna is horizontally polarized, and a 2M/440 vertical antenna is vertically polarized. Simply put, this means the antennas "see" on planes perpendicular to each other. This will greatly reduce (attenuate) the amount of RF energy passed to your TV antenna when you transmit.
EDIT: Also, your TV antenna being directlt under the vertical puts the TV antenna in a null of the radiation pattern of the vertical, which means the least amount of RF energy possible is radiated in that direction. I can E-mail you a screenshot from my antenna modeling software to demonstrate this if you like.
2) VHF TV operates just above the 6 meter ham band (50-54MHz), while 2M is higher in frequency (144-148), UHF is even higher (420-450MHz) These signals will be further attenuated in your TV antenna because it is not tuned to recieve those signals. The exeption will be if you watch UHF TV, which is very close to the 440 band.
I used at my old house, a diamond SG-2000 2M mobile mouned right on top of a TV antenna with little or no RF interference TO THE TV, however, stereo and computer speakers picked up a hum. I ran 50 watts at times with no damage. In fact, the TV antenna acted as a ground plane for the vertical, focusing more of my RF towards the horizon, yielding a better signal (higher gain).
I doubt you will do damage, but you may desensitize the reciever in your TV when you transmit. It would be wise to test at lower power levels first.
Let me know the results, I'd like to compare them to my own experiences. If you have any other ham related questions, don't hesitate to PM me.
Your friendly neighborhood Extra,