To install Sourcetree you'll need a network connection in 2 occasions: first, to download the software; and second, to complete the registration. Once those 2 steps are done, you'll be able to use Sourcetree without any access to the Internet at all.
If you're not allowed to access internet from your network, you will need to use a different one just to complete the registration, maybe at home, or in a café.
Hope that clears your questions, Luca. Let us know if you need anything else.
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