Probably but not clear what it is
327 is mentioned a lot in Star Wars, so there is obvious some significance.
As well as the Docking Bay on the Death Star and the Landing Platform on cloud city that you have mentioned, there is also the following mentioned in Canon:
- The J-type 327 Nubian starship used by Queen Amidala - which had a Nubian 327 hyperdrive core in The Phantom Menace
- The Vulptereen 327 Podracer that Dud Bolt raced with in The Phantom Menace
- The Rian 327 Airspeeder owned by Padmé Amidala in The Revenge of the Sith
- Outpost 327 where the shuttle Tydirium was stolen from according to the Junior Novelisation of The Return of the Jedi
- The Hurid-327 Load lifter droid at Maz Kanata's in The Force Awakens
It also had many further mentions in Legends materials.
The number makes an appearance in Lucas' earlier film American Graffiti where the '32 Deuce Coupe had a Chevy 327 engine, this car also had the number plate THX 138 - (a reference to the even earlier Lucas film THX 1138
I cannot remember nor find any mentions of 327 in THX-1138 nor in any Lucas related films after Star Wars (Indiana Jones, Willow etc)
So it appears to be something brought into Star Wars & kept within that universe, unlike THX-1138 which has appeared through most of his works.
It is possible that this is a nod to the film American Graffiti, whose commercial success gave George Lucas chance to develop LucasFilm, Skywalker Sound, and Industrial Light & Magic which were all crucial in allowing Star Wars to be made.
As an aside the hatch number for the trash compactor 326-3827 is widely reported to have been Mark Hamill's phone number. This has a symmetry with THX 1138 which (using the keypad map of T=8, H=4, X=9) was 849-1138, George Lucas' telephone whilst at college.