Yes for many airlines, but not for all of them, so it comes down to which airline your customer is flying. Where the airline shares its seat map with us, the seat step appears during checkout, your customer can see the cabin layout and choose a window or an aisle, and that choice goes to the airline with the ticket. Where the airline does not share a seat map, the step is skipped and the seat has to be sorted out at online check in instead.
How the seat is charged also varies. Most low cost airlines treat every seat as a paid extra, so the amount is added on top of the fare and collected in the same payment as the ticket. Network carriers often give a free seat in economy and charge only for the better rows, such as extra legroom or seats near the front. Whether that charge can be taken in your checkout or only on the airline site depends on what the supplier behind that airline allows.
It is fair to treat a seat as a request rather than a promise. Airlines can move passengers when the aircraft type changes, when a flight is retimed or for operational reasons on the day, and refunds for a paid seat in those cases are the airline's decision, not ours. Seats on flights that are sold by one airline but flown by a partner are usually not available at booking at all and only open up at check in.
Before you start selling, run a few searches on the airlines you sell most and see which of them actually show a seat map, then tell your customers plainly that a seat is only certain once it shows on the airline's own booking, and remind them to check in online as soon as it opens.