Yes, if the player device (TV in this case) will play it from the PC, then they should play it from the hard drive. As I said before the drive itself is merely providing the file, it isn’t playing it. You should get out of the habit of referring to the drive as playing the file, or you could confuse things.
The only other caveat to be aware of is if you set/enable stuff like encryption or locking up on the drive (basically stuff that needs the special WD SES driver) then your TV won’t be able to use the drive directly, as it won’t have the driver in place to do the decoding (and WD don’t make drivers for stuff other than Windows or Mac). But if you just keep things simple and use the drive plain without enabling such driver-requiring special features then it should work.
This is one of those cases where you need to be a little selective about which drive you purchase, as WD do a range of them with various features, and if you are going to be using it at a basic level without such features enabled then there is an argument to go for the cheaper (MyPassport Elements) drive that doesn’t have them over the more expensive ones (MyPassport Ultra) which does. You can use a MPU with the TV, but all the security features will need to be turned off.
It may also be worth checking how much current/power your TV USB port provides, to ensure that it is enough to run the drive. The WD portable ones are powered by USB, and if the TV doesn’t give enough juice then you’d need to put a powered hub in there too, and that is sometimes known to cause issues in itself.