I wouldn't consider a PB run on a treadmill a real PB, but if the treadmill is close to calibrated I'd imagine someone who ran 18 min 5K on a treadmill should be able to run at least a sub 19 minute 5K on the road.
One thing to keep in mind with Strava treadmill posts... when I run on the treadmill with my Garmin watch the watch measurement does not match what the treadmill says. The Garmin pretty much measures off cadence and my treadmill pace varies between 9.8 mph (6:07 pace) and 6.8 mph (8:49 pace) depending on what I'm doing on a given day... meanwhile my cadence barely changes so my Garmin can be way off. On the Garmin you can recalibrate based on what you actually ran on the treadmill but the Strava post won't reflect this...
...the long story but my point is that with treadmill posts on Strava, who knows what's going on... I know for me personally my distances can be +/- 1 mile off... I don't make any effort to note this in my workouts or change anything because I don't care that my strava treadmill run is inaccurate. Maybe you shouldn't care either.
To answer the question I'd say that treadmill running is real running. I build a ton of aerobic fitness on the treadmill over the winter and it beats the crap out of suffering on the dark, cold, windly, icy, roads. Once spring comes, instead of being burnt out by forcing myself out in miserable conditions, I'm instead super motivated to dominate some training on the roads with a strong foundation to build on.