Sure you can very slowly get better playing very fast chess but you can quickly get better playing slow chess!
Of course it's always easier if we ignore all those people who start out playing a slow game then, after spending an hour of their life losing just lose interest in chess completely!
For a current research project, I'm studying how different chess players use their training time. If you are an active OTB player with a FIDE rating above 1000 (or a national federation equivalent), then you are invited to take the survey linked below. The survey will take no more than 10 minutes. Thank you!
Link to Survey