Yes but don't expect them all to succeed. Maybe none will become a plant first time which is why many people just buy small plants rather than doing it from seed themselves.
I actually like to keep seeds from everything I grow. I dry them, bag them in see through zip-lock bags and label them with name and date. I love keeping the seeds from a plant gifted to me to then end up with lots of them without ever buying a pack of seeds. Same applies to bulbs - which multiply. Children need to be shown how to take cuttings of many plants also. If they end up with too many they can donate them to any organizations having a fundraising event. When my kids were in school I donated dozens of small plants for a stall at every fund raising event. A teacher would call at the house to collect them as they always sold really well.
It's amazing how many of us, when kids, after the war, kept acorns, conkers, seeds from pine cones and fruits we'd eaten and tried to grow them. Some succeed and some don't but it's great to try and watch the wonders of nature unfold before our own eyes. Too many kids these days have no idea where our food (or flowers) come from. The next generation of youngsters are going to be very ignorant human beings I'm afraid.