Most likely not, not with this TP and this board.
To get deeper into the subject of why i would and why i wouldn't donk bet this or that first i need to ask you what was the reason for your bet on flop?
we need to know why we bet, do we bet for value or we bet as bluff, for example if i opened 66 bvb and face this excuse for a 3bet i would call with nice odds
to setmine, i would probably 4bet shove for value TT+ maybe even 88+ but here i hypothetically called and hit set, now i want the pot to get bigger and eventually to get all the money in and i cant do it if i check and let him check back cuz he didnt flopped to much but draws and medium hands which would likely check back flop but would call cuz pot odds
or auto raise cuz thats what you should do against fish who donks (we appears as a fish here, in his eyes) and here we get value and get the money in, if he called the pot is bigger and we can put another barrel, eventually snap shove to appear weaker and here money are in, value is accomplished. With TPGK on this board i would probably went into x/c mode to keep his range wide and depends of the sizing and canrd to come i would do that on turn or river or not...