Yes, campaigns in Tanganica can run alongside your own or your agency's campaigns. For smaller e-shops, however, we recommend running Google ads only in Tanganica, see How campaigns in Tanganica.com work for the reasons. For larger e-shops with a high number of orders, running both can make sense, because under Google's rules the campaigns don't compete with each other and don't raise your click prices.
For details on how this works and what the benefits are, see I already have my campaigns and I'm afraid that it will compete with Tanganica campaigns.