The seeds are unlikely to 'come true' but if they do, it may take four or five years...maybe longer.
Whether you decide to let them ripen off or not is up to you, but they will deplete the bulb's strength....
EDIT NOTE:
By the way, if the flowering bulb you are growing, is the huge one with the big trumpet-like flowers at the top of a thick, tall hollow stem, then strictly speaking, they are better known as "Hippeastrum".... Check this page out....
http://www.rbgkew.org.uk/plants/springbulbs/hippeastrum_prop.html