used to work on a similar project in my day working for a large cow spotted computer manufacturer. We were concerned about emi more than you may be. My quick answer would be yes, it may cause issues.
It would depend on how much shielding is on the tube components themselves and how much they used the metal case for sheilding.
I am surprised that there seems to be enough room for Board/Powersupply and HDD. I would also be concerned with how I mounted those items to the metal case (grounding issues).
To be safe, I would try to make a thin box to go under the TV, attach the 2 together and go from there.
I may be wrong it may not have any problems, but I would be careful.