Yes - the company "churns" your line for you so there is no break in service. It all still goes through the PSTN so basically Hellstra just change who they are billing on X date for your line.

If the co you are going to uses a different company for STD/IDD (eg: Telstra Local/Optus Long Distance) then make sure you check your first bill for Local calls. If they arent on there make sure you keep some cash aside for them as they will be on the second bill. It shouldn't happen as LOLO has made the churning system simpler, but I always warn people just in case, else their first to second bill fluctuation can come as a rude shock.