I read in the description of Starshine Lunacy's youtube video of this level that... 

"That archvile jump onto the blood fountain is pretty annoying, but it's not optional for killing him"

...and I decided to see. 

So, it is possible, but really RNG dependent and really annoying. 
I lowered the WR time while i was at it, so it is viable, but you could save at least a minute by preforming the jump instead. 

The thing that had me restarting this map more often than not were the triggers for the doors at the start, and the triggers for the teleports. I would skip the linedef for the doors if i was moving too fast, and sometimes enemies would get stuck in the off map rooms (esp the SS guys which is why using splash damage to kill the archie in a reasonable time is a dice roll)

Anyway, yeah, wasn't out to set a world record, but I did, neat. 
I don't expect it to last very long, as this run is far from optimized and just preforming the archie jump would save almost a minute. 

But, I proved a point, and ill take it for now. 

Sorry Starshine :)
