Hi Heather, I assume you mean the regular garden
variey geranium. Removing the dead flower heads
including the stalk of course makes the plant
prettier. Letting it go may produce seeds, but
also may drain the health of the plant.

You don't need seeds to propagate, and since
yours is healthy and thriving I recommend when
it reaches a size where you can take cuttings
that is the best way.

Try to pull the cutting off at the place
where the branch meets the stem. Let cuttings
dry a day or so (contrary to most other plants).
Then stick them into good potting soil and
keep barely moist until roots start to show.
They usually root easily and soon you will have
tons of them.

Anne