Might I have any problems if I use my wallet (I'm intending to use Tails on a pendrive with persistent storage and Coinomi) through Tor with them?
There are few possible problem/inconvenience (you need to verify the possibility by yourself),
1. I don't know whether Coinomi server (which serve data such as transaction history) allow Tor user.
2. Tails block application from accesing internet unless it's configured to user Tor. I don't know whether Coinomi have option to use SOCKS5 proxy.
Packages that use the network need to be configured to go through Tor. They are otherwise blocked from accessing the network.
3. You need to configure Dotfiles (
https://tails.boum.org/doc/first_steps/persistence/configure/index.en.html#index13h2) to preserve directory/files created by Coinomi.