Yes, in most cases you will see an airline booking reference for a flight sold through your portal, and you can usually use it to look the trip up on the airline's own site. When the booking is confirmed, the supplier sends back a reference, and once the ticket is issued the ticket number comes back too. Both normally appear on the booking details screen in your admin area and on the confirmation your customer receives, so you have them without having to ask anyone.
Whether that reference works on the airline's website depends on the airline and on where the fare came from. For most scheduled airlines booked through a normal flight connection, the reference is the same one the airline recognises, so you or your customer can enter it with the surname and then check in, pick a seat or see the latest schedule. With some consolidated or aggregated content you may only get the supplier's own reference at first, with the airline one appearing after ticketing, and sometimes not at all. A number of low cost airlines keep the booking inside their own system, so the reference is only useful on their site.
One honest word of warning. Even when you can see the booking on the airline's website, making changes there directly is risky, because the supplier record your portal relies on will not know about them. That mismatch is what causes problems later with refunds, date changes and extra bags. Treat the airline site as somewhere to look, not somewhere to act, and send any change through your portal or your supplier so everything stays in step.
Open a recent flight booking in your admin area and see which references are stored against it, then ask each of your flight suppliers whether they allow you to contact the airline directly for servicing.