I say yes. I enjoyed Star Trek Beyond quite a bit. I think it was a movie that did poorly at the box office simply because it was released at a bad time when there were a lot of other franchises trying to launch big summer tent pole movies.
I also enoyed STID, but not as much as Beyond and the first Trek. Fans could see the rehash of TWOK coming a mile away. (And no disrespect to Quinto's Spock performance at all, but the KHAAAAAN moment was the only time I had cringed seeing a Star Trek movie in theaters.) Despite the occasional plot issues (aft nacelle) and the unfortunatel circumstances involving the passing of the amazingly talented Anton Yelchin, it will be difficult but not impossible to produce a good Kelvin timeline sequel.
Beyond was the end of the 5 year mission. This is an area of Trek that has not been explored all that much. The time when Kirk was promoted to Admiral and left the Enterprise. I wasn't born during the 60s/70s when Trek made the transition from TV to film, but I do not believe there is a lot of concrete info about what happened when Kirk became an admiral. It would be feasible to do a Kelvin sequel with Captain Spock and the rest of the TOS crew, perhaps with Admiral Kirk as a cameo or a more prominent role should Paramount sort out the contract issues with Chris Pine.
Unforunately, Chekov would need to be recast or retired, but again could be explained away as Chekov did eventually join the Reliant crew in TWOK. Chekov also wasn't around for all of TOS, which is something I just recently learned through watching the show for the first time from start to finish during the 50th anniversary. I am ok with either option so long as it is done tastefully and with respect to Anton Yelchin.
In any event, a post TOS/preTMP Kelvin film can be made and would provide the producers and writers the chance to tell an original story that is not as restricted by canon.