Does an outdoor channel drain need a p-trap?

We are closing off a basement entry door that is at the bottom of a short flight of concrete steps. This is a newly purchased older home and I think there was some question as to whether those steps were occasionally allowing water into the basement or not. Since it's a possibility / probability that there is at least occasionally leakage here, I would like to address it before we seal off the door.

The idea I have (and tell me your better ones!) is to place a channel drain where the last step is and pour new concrete around it. This would give me the height necessary to drain into the nearby stack base without having to break up the slab floor.

Assuming this is a sound plan, what are the issues with sewer gas getting out the drain. Obviously it'd be outdoors but the location may be just below a kitchen window and we'd not want any off smells of course. Do I need a ptrap? Would one work?

FYI, the doorway of course penetrates the concrete foundation. We'd be filling in the doorway with a wood framed wall, osb sheathing and new siding (another benefit of the concrete pour would be that it separates the siding from the ground.) Finally, over the old steps will be a new cedar deck with open-draining slats.

What your proposing is against code. You cannot drain storm water into your sewer. A better idea would be to have the storm drains around the house camera'd. Then have them flushed or repaired if needed. If they are ok then put your drain in and tie it into the storm.

My 1950s house does have a drain in the basement stairwell than terminates in the sewer that was constructed when the house was built. That drain has a trap.

Making one of these now, however, would not be allowed. And the drain I have is far from a perfect solution. For example, it allows any dirt or junk in the run-off to enter my sewer pipes which requires snaking every year or so.

So here are two other ideas.

Could you construct a drain that terminates in a sump pit, if you have one?

Could you add a drainage system to the cedar deck, so that as that drains it diverts the water away from the stairwell? They do sell these which attach to the underside of the deck.

Your proposal is just asking for trouble. You will NEVER make the opening watertight, and you will be creating a spot for every piece of garbage to blow into, which would eventually block the drain. Use cement block to seal the opening. Waterproof the outside, and then bring in dirt to fill the stairway level with the ground. FINALLY, build your deck over it.