There was a sudden movement behind them. Gilderoy Lockhart’s knees had given way.
‘Get up,’ said Ron sharply, pointing his wand at Lockhart.
Lockhart got to his feet – then he dived at Ron, knocking him to the ground.
Harry jumped forward, but too late. Lockhart was straightening up, panting, Ron’s wand in his hand and a gleaming smile back on his face.
‘The adventure ends here, boys!’ he said.
Chamber of Secrets - page 224 - Bloomsbury - chapter 16, The Chamber of Secrets
Gilderoy Lockhart took Ron Weasley's wand by force.
Did Ron's wand switch its allegiance to Lockhart or not?
I'm looking for an answer based in wandlore, not a quick "Because Ron's wand was broken" one-liner with no supporting explanation, canon references, or wandlore. I'm interested in hearing about how wandlore and damaged wands might work together to affect the ability of a wand to change its allegiance -- I'm sure Ron's wand being broken could have been a factor either way, but why and how? Subjective answers with wandlore and the spirit of canon are totally fine. I'm not looking for any HP Wiki/Wikia answers.
ETA: I was talking with DVK and he indicated my question sounded like I had already made up my mind that Ron's wand did switch allegiance. I have edited this slightly to be more neutral because I don't have an opinion on whether the wand switched allegiance or not. That's why I'm asking. Hopefully my clarifications will help.