Of course they can, but many ban waves hit during maintenance/patches. It allows the devs to add more detection methods to the game too. Basic rule of thumb is to not use any trainers right after a patch until its confirmed to not be detected.
Lol what bans? BattlEye is only enabled in the Ghost Wars PvP mode of the game. Unless you are using the trainer in their SEPARATE PvP mode online which is against CH's rules as well as Ubisoft's and Battleye's you won't get banned at all.
If they wanted people to get banned for no reason during single player and coop play they would have re-enabled Easy Anti Cheat or went on Steam and enabled VAC.
You have no idea what else is running, or what other parameters they may use to flag and ban your account. I would assume that people NOT going online to play with others in PvP are likely ok, but I would never say that we know for sure. These games may have other things in place that are detecting cheats and/or flagging certain conditions.
use trainers and mods on these sorts of games at your own risk. We have no idea if/when/how they will flag and/or ban for using trainers and mods with this game. We've done all we can to try and explain to NOT USE ONLINE WITH OTHER HUMANS and to explain the risks, etc.