I currently use one of those flat pieces of coax with my APRS digi. I live in an apartment, and my feedline goes out along the floor via RG-8X, under a regular hinged exterior door via the piece of flat coax, then back to RG-8X onto my balcony and up to my antenna bolted to the railing.
I have not tested SWR (scared to) but it works well enough to cover a big chunk of the northern Virginia area. I regularly transmit 25 watts through it (60+ once or twice) with seemingly no ill effect. Well, my FT1500M hasn't blown up yet at any rate.
One word of caution, the jacket material is rather thin and will crack over time, letting moisture in.
It is a decent temporary measure but if I were you I would go forth with one of the more robust alternatives described in some of the other replies.
I'll soon be getting rid of mine and drilling a hole through the wall for a proper coax passthrough.