Yes, in most cases the low cost airlines can show up in the same search as the full service ones, so your staff only work in one screen and compare everything side by side. The search goes out to all the sources connected to your account at once and brings the results back together, sorted by price or timing, and your agent books whichever option the customer picks without switching to another website.
What is worth knowing is that the two types of airline behave differently once you get past the search. Full service carriers usually come through the big airline reservation systems, while budget carriers are normally connected directly to the airline. That means budget fares are often sold as separate one way journeys, bags and seats and meals are nearly always paid extras rather than included, and any change or cancellation has to follow that airline's own rules rather than the usual ticketing rules your staff may be used to.
I should be honest that which budget airlines you actually get depends on the suppliers connected to your account and on your plan. Some carriers do not sell through travel agencies at all, and others only allow it under their own arrangements, so nobody can offer you every low cost airline in the world. Payment can differ as well, since certain carriers want the card charged at the moment of booking.
The best next step is to send us the list of budget airlines your customers ask for most often, and we can tell you which of them are available on your setup before you start selling.