If you are using the hood, there will be precious little room between a 77mm filter and the hood, and it will be annoying to get on and off.
Precious little is an understatement. I tried it myself with my 135mm f/2L and B+W 72→77mm adapter with a 77mm filter on it. As stated, the hood will not fit over the 77mm filter. With the hood installed, there was really no way to thread on a 77mm filter inside it - it could be dropped in, but there's just not enough clearance to screw it on inside that hood.
I should point out that this is not true for all lenses with 72mm threads - I have the 85mm f/1.2L II, and often use a 3-stop ND filter with that lens. My filters (except UV) are all 77mm or 82mm, and with the 72→77mm adapter, the hood for the 85L can be installed over the mounted 77mm filter. Also, the 200mm f/2.8L II (which I had, but sold after getting the 70-200mm f/2.8L IS II) is quite similar in design to the 135L, but for that 72mm-filter lens, the hood can also be installed over a stepped-up 77mm filter (the 200/2.8 uses an 83mm hood, vs. the 78mm hood for the 135/2).
Like epsiloneri, I have never felt the need to mount a CPL on my 135L - it's just not needed for the type of shooting I do with that lens. However, it occurs to me that I'll probably want to use an ND filter with that lens, for the same reason I use one on the 85L - outdoor portraits in bright light (or with strobes) where I want to open the lens up. It hasn't come up yet since I bought the 135L in January, and it's been too cold for outdoor portraits - but spring is here, so I may have to get a 72mm B+W #103 for outdoor work with the 135L. In fact, since I bought the 35mm f/1.4L at the same time as the 135L, I now have the complete 'holy trinity' of L primes - and they all use a 72mm filter. So for me, I think a 72mm ND would make sense. But still, for a CPL almost anything I'd be likely to shoot would be with a narrower aperture, so I'd likely use a zoom with a 77mm thread for those shots.