A couple of things to consider:
We don't have a lot of established PF in this area, so people's opinions vary wildly based on what their own assumptions are.
I'm going to go with yes, ship boarding happens, see that previously linked marine item.
Points of Intereset:
1. Capsuleer vs Non Capsuleer ships:
Boarding a non capsuleer or civilian ship is likely much easier; The capsuleer likely has intimate knowledge of every nook and cranny of their ship and would be a fantastic medium to direct a counter boarding response. Capsuleer ships also have the latest and greatest technological whizz-bang devices, so I would expect expensive capsuleer ships, especially the large capital ships, to be full of all sorts of nasty marine teams, automated turrets, and difficult-to-overcome obstacles around critical ship areas. Larger ships from empire navies also full of scary things to shoot boarders.
Capsuleers are very unlikely to allow their ships to be taken over by baseliners; they can always pull the plug and blow the ship, unless they have sentimental attachment to valuable cargo or personnel. Now I personally leave room in my little lore universe for special cases to ruin a capsuleer's day and control over their ships. I have to imagine if we have giant modules that can remotely 'remove' energy from a targeted ship, then perhaps fancy whizz bang technology to snap a capsule's connection to a ship, or maybe even remove the power from the pod gantry for escape purposes Who knows, plenty of possibilities here.
Non capsuleer ships are probably getting pirated and captured 'erry day in scary parts of space. Sanshas, Blood Raiders, regular pirate folks, lots of hunting on the space lanes. Boarding and capturing some hauler out of lowsec full of 'civies and refugees is likely not especially difficult for some of the more hardened space killers out there.
2. Why board a ship?
Steal Cargo. Steal people. Kidnap a VIP. Take the ship. All good reasons. One wouldn't board a ship to destroy the ship, as there are a bazillion better methods that many of us use on a daily basis in PVP (blast them until they explode).
3. Gravity
I'm going to assume with handwavium that ship's gravity is much more of an 'on/off' sort of duality, or very difficult to control on localized basis. 'artificial gravity' is a damned ugly handwavium in lots of sci fi; it's convenient and easier to have people walking around on spaceships that resemble earth naval ships than to really deal with the annoying zero g aspects. People in eve have artificial gravity control, but they don't weaponize it. I call this pure handwavium, assume the gravity control is complex and not easy to manipulate aside from amarr hover-chairs and cars, and try not to think about it. Otherwise shit gets complicated really fast for weapons and combat and we don't see any of that in EVE so far.
3. This is all RP conjecture
None of this is reflected in gameplay and is entirely in our own little RP head space. There is no ship boarding gameplay, and until they weave Dust into capturing stations and pos, there won't be.
So lore-wise it happens, although not in any detail that we can agree on and it's strictly in our heads as to specifics.