No, I don't think so, It was kind of faraday cage to protect humans from the spider. Webber broke it and spider attacked im. I believe it because we saw same similiar "getting creatures from DST world" thing on one of the puzzles. Maxwell somehow teleported a rabbit to the world. So that shows teleporting creatures from that world to our world is kinda easy.
Waggstaf got the spider somehow and took it someone know spiders biology better for further research, like Webber's dad. I understand he is probably kind of entomologist on the start of trailer and I became sure when see all that bugs on his wall. If even he is not, he is kind of zoologist but entomologist make more sense to me.