Absolutely. I personally use neodymium magnets to hold my branches up in my screen enclosures.....mainly because I have this strong resistance to poking holes through something I just paid money for, lol. I would say the majority to people attach the branches with push pins through the screen or fishing line/zip ties.
Hanging the plants....you can either buy Dragon Strand Ledges(which are awesome) or you can run a dowel across the top of the enclosure and tie a piece of monofilament to it. Run the monofilament through the screen top and attach it to the hanging apparatus of the pot. Of course you want to make sure the dowel isn't sitting on the screen itself, but rather the edges of the enclosure.
What size enclosure do you have?