Be aware, that as the strings get thicker, the nut slots will be more likely to bind. This doesn't mean you should switch back to thinner strings. But it does mean that you may need your guitar tech to do a little work on the nut in your next setup. But in the mean time, some Big Bends Nut Sauce (or similar lubricant) might get you through.
As for the neck joint on an SG, my 68 SG was my slide guitar, so had 12's set up on it for years and years with no issue. It depends on the guitar, but I would be shocked if any SG couldn't handle 11's or ever 12's.
These days, it is no longer dedicated to slide, so I have 9's on it.
No issue with nut slot binding whatsoever and I am sure this is the original nut from 1965 on my SG Special and I am good at overall setups.
So far way less tuning issues with 11's vs. 10's.....my neck is thick past the first few frets.....if I have a problem with the neck joint, I will repair it.
I MUCH prefer the tone & feel on the wound strings with the 11's....maybe its the balanced tension D'Addadrio 11 set......I dunno.
I do intend to downtune which is partly why I made the switch from 10's to 11's.
I tried downtuning with 10's...sounded and felt like crap.