Of course it will - outdoor-safe fabric is just a solution dyed synthetic fabric. It's not a magic fabric! Is it Sunbrella, or a similar?

Unless it's hugely heavyweight (like a tent fabric) sew it like an ordinary fabric of the same weight.

I assume by "outdoor thread" they are speaking of a heavyweight poly or nylon upholstery-weight thread. Yes, that is a good idea. Use an appropriate sized needle and increase your stitch length.

Oops - I now see that on another posting you were asking if a domestic machine could use this "Outdoor Living" type thread. Again - these are not magic fabrics or magic threads.

So short answer - yes. Long answer - use a large needle - I would use a topstitching needle. I like Schmetz 12/80 with an elongated eye. 14/90 will also work.

Increase your stitch length from 10-12 stitches/inch to 6-8 stitches/inch. Stitch at a medium speed. Check tensions carefully, and understand which one might need to be adjusted.

Here is a link that might be useful: Schmetz needles