It's almost certain that she would.
Although she didn't always live on the Square, Dot has always lived in Walford, apart from brief period she spent with Nigel in Scotland.
Dot knew Den "growing up", I would also imagine Kathy and Gavin's backstory has them meeting in Walford all them years ago, as she was best friends with Angie and Den, working in the Queen Vic with them for a while.
How Sharon came to be adopted by Den and Angie, will be an interesting tale for EastEnders to explore. I would also bet my life that the solicitor Sharon went to see the other day, is in fact Gavin's sister and therefore Sharon's biological aunt.
But yes, Dot and Gavin meeting should be an interesting one. I don't expect them to be close or have an awful lot of history together, as Gavin left Walford when Sharon was a little girl and hasn't been back until now. Dot wouldn't have the history with Gavin, that she had with Den.