Yes, the Flame Trap system applies manifold vacuum to the crankcase.
Yes, it would pressurize if there were no form of ventilation or breather system.

Removing the screen only clears one of the many components of the breather system - but only that one.

A clogged flame trap blocks the existing ventilation/breathing system and will cause crankcase pressure to build - an all-too-common situation in bricks due to some owners & mechanics either not knowing or caring about the flame trap system.

Reportedly Volvo has stated that you can remove the screen from the flame trap. I can't confirm this.

Since your 240 is more than a couple years old, it probably deserves a good overall cleaning of the whole breather system.

If there are any oil leaks, it's best to service the crankcase ventilation system fully to make sure that's not the cause of the problem. Look in the 700-900 FAQ for details, under Engine - Seals and Crankcase Ventilation or something like that. It's there, in extensive detail.

The upper part of the flame trap system has the flame trap screen, its holder, two hoses, and a brass nipple for the thinner hose. They are ornery enough to get to, but doable. Clean these up per the FAQ and see if your leak clears up.

Below that is another hose (about 5 inches, "S" shaped), the breather box, and two openings down into the crankcase, one of which has a hose/tube within the crankcase. If your leak doesn't clear up, you should ensure those lower components are clear. Note that simply blowing air down into the breather box via it's top hose - and noting that the air comes out the (removed) oil filler cap - does NOT necessarily indicate that all passages are open. There are two paths out of the bottom of the breather box into the crankcase; if one is blocked you will still have air through the filler cap but a malfunctioning breather system.

In my case I took the better part of a summer Saturday to go through all of it, cleaning the idle air control and throttle body at the same time (IAC had to be removed anyway to get to the breather system, etc.). When done, I had full confidence the system was clear, but still had a rear main seal leak. So I paid the shop to replace the seal.

Re. the tube/hose down into the crankcase: It's likely fragile and brittle by now. I cleaned it very carefully, as breaking the tube requires much more work to repair that new damage, as in "remove frame cross member and oil pan". I first trickled some GUNK motor flush down the tube (requies an oil change afterwards), then probed carefully with a soft, rubber-insulated electrical wire (no metal protruding), then with a thick-stranded poly rope about 3/16" or maybe 1/4" diameter. When the rope came up with oil in it, I knew it was OK.

I sprayed into, poked into and whacked on the breather box until it was clear to my satisfaction. It's far eaasier to buy a new one.
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Sven: '89 245, IPD sways, electric rad. fan conversion, 28+ mpg - auto tranny. 850 mi/week commute. '89 245 #2 (wifemobile). '90 244 (spare, runs).