Permitting Teams on non-enrolled devices

Currently our users can access Office 365 in a browser on non-enrolled devices, but they are prevented from downloading and uploading files etc. 

I am now trying to find out if the same functionality can be achieved with the Teams app: allowing users to log on to our tenant in the Teams client app on non-enrolled devices and preventing up- and downloads. If we exclude the Teams client app from the conditional access policy that requires the use of enrolled devices, will that also allow users to up- and download files in the client?