I couldn't find much on the documentation, and I have never used this feature before, but I've found a lot of people[1][2][3] who couldn't get it to work with the testnet mode.
EDIT: I've also found
this. According to Bauerj's answer, the cosigner pool should be functional on the testnet (unless servers are down). If you're facing some persistent problems with it, it might be a good idea to open an issue on the Github repository, you will get more help there.
[1]
https://www.reddit.com/r/Electrum/comments/d7r2ax/is_it_not_possible_to_use_the_cosigner_pool/[2]
https://bitcointalk.org/index.php?topic=5125807.0[3]
https://www.reddit.com/r/Electrum/comments/79ofg0/genuine_multisig_problem/