On a televised candidate forum prior to the 2016 election, The Former Guy said Putin "has been a leader far more than our president [Obama] has been". When asked about his previous complimentary remarks about Putin, TFG replied "He does have an 82% approval rating" and that he had "great control over his country".
The fact that praise for and defense of Putin and unflattering comparisons with Biden is splattered all over the rightwing news and social media indicates that yes, some of them do. Anybody remember the "better Russian than Democrat" t-shirts? Tucker Carlson's simpering over Viktor Orbán? There has been a general movement on the right worldwide to praise the rising crop of autocrats for their nationalism, "Christian values" and anti-immigrant positions.
A better guess is that most of the GOP base wants to hear the current POTUS "maligned by public comparison" to the Russian autocrat. That's not just based on my instincts - clearly the conservative elite class either thinks it plays with the base or wants it to.