Short answer is yes, they can. We can't prevent users from doing any changes to their signature in their Gmail Settings. 

Maybe you've stumbled upon the feature enabling the users to change their signatures in Settings that gave you this idea:

The default option is set to "Users cannot directly update their signatures". If you change it to "Users can directly update their signatures", and your users perform any changes in the User form, these changes will be automatically reflected in their signature - but be careful, if you use credit system, you'll be charged for this action. There's also a possibility that the user might do inappropriate or othwerwise harmful changes, so unless you trust your users completely, we suggest keeping the option set to default and review the requested changes manually.

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