While on a Dispel Virtual Desktop, users can connect to internal network resources, but have no access to external internet.
Could I get Internet access?
If you REALLY wanted to, yes. What Dispel is doing is providing a temporary SD-WAN within which remote access activities can take place. An administrator can place a portal to the Internet at large on the SD-WAN.
Can I allow some internet access, but only to specific sites?
Yes. Just add those specific IP addresses to the whitelist, and they will become accessible. Everything else will remain unreachable.