I don't imagine so. His style was a bit antiquated and his assets match up poorly to Wlad's. You can't just glove block Wlad's punches. They split the guard of practically every fighter he faces. And Jack's greatest asset was his strength. Well, I know one guy who he is not stronger than. Every guy who faces Wlad attests to his ridiculous strength, strength befitting the giant he is. Also, Byrd was plenty cute, if not cuter than what we see of Johnson on film, and Wlad just steamrolled him. Once Wlad get's him at the end of the jab, it's just punishment time. Though it is more than just size here (it is how their strengths match-up and the techniques both use(d)), realize that the best fighters Johnson fought McVea, Jeanette, Langford, Burns were leagues smaller than Wlad. Johnson's greatest advantage against his best opponents was size and strength. He isn't getting that advantage here.
If Ketchel managed to land his looping amateurish right then Baer can land his too, except it would be landing with force Johnson would've never before encountered, taking into account Johnson said the hardest puncher he fought was Super-Middle Choynski.
Johnson would pick Baer apart. Baer did not have the defense to stop any of Johnsons blows. Also JJ would see all of Baers punches coming from a mile away. In a 20 round fight it would be a gradual beat down with the ref stopping the bout after 13 rounds..Baer beat to a pulp and JJ unmarked and virtually untouched.
Prize ring rules means they can do hip throws and ****. Johnson still trained that, and often wrestled with top guys. I don't think Baer did much wrestling even for training (by his time they had started to do less of that). Johnson would work him into clinches and throw him down. Several throws on a man not used to taking falls would eventually result in a fight ending injury and a win for Johnson.
Luis Firpo's camp threw Johnson out after he made Firpo look foolish in thier sparrng sessions and Jack was in his early forties at the time. I think a prime Johnson frustrates the hell out of Baer and boxes his way to a decision.
At his very best Johnson was nigh unbeatable to those weighing similar. Had there been a 20 round limit he'd likely have remained champ until Dempsey came along. Baer is a few levels below Johnson although his size and pressure could pose him problems (hart fought even with him afterall). I think at his very best Johnson was a true heavyweight (Jeffries fight) and that version should stand up to Baers aggression and out point him. If Johnson comes in lighter like his early days we could see Baer force the stoppage. Peak for peak I take Johnson though.