Sure: https://licensecart.com/billing/plugin/support_manager/knowledgebase/view/3/how-can-i-get-a-direct-url-to-a-package/11/
If it doesn't work because of the domain issue you could add it as a feature request or add it to the one about products first domain after.
You need to ensure you are using the domain and other type order form.
The client can enter the domain and register or transfer the domain to you. If they want to use their own domain they can click on Order other items and skip that part and can buy a package after.
If they are buying a domain the domain section for the shared hosting is automatically filled in ready. If they don't order a domain they can enter their domain manually.
Welcome to the Blesta family I know how you feel I keep telling Paul I regret not using it back in 2008 with Blesta 2.x much better than that rubbish called WHMCS.
If client is logged in:
Show Blesta menu (log out, dashboard, support tickets, etc)
else
show your menu (home, about us, services, etc)
You can see the if statement on the tutorial and see it in action on LC.
It might be something to do with the bootstrap JS, or the css mixing with the top. I would recommend you to change the menu at the top when a client is logged in. So you don't need to worry about that.