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Not at all. In addition to that, if you remove the flowers as soon as they're finished blooming, you'll not only prevent the formation of seed pods completely, but the plant will be encouraged to make more flowers because it won't be putting energy into making seeds.

Rose of Sharon is actually a variety of hardy hibiscus. Therefore, pruning takes place in spring--specifically anytime from late March through early May, before the leaf buds open. Overgrown shrubs can be pruned back to about three feet in height without risk of injury. Then you should perform annual trimming to to keep its appearance maintained, removing any unsightly or overgrown branches only. Here is more info: https://www.gardeningknowhow.com/ornamental/shrubs/rose-of-sharon/pruning-rose-of-sharon.htm

You can prune rose of sharon pretty hard because, as you have seen, they grow very quickly. It would be best to prune them in the spring and this will not affect its ability to bloom.

Rose of sharon is a very easy plant to care for. They do best in full sun (6+ hours) but will do fine in part sun (4-5 hours) and can also manage somewhat shady conditions. After they are established, they need almost no fertilizing or extra water, but if you are concerned they are not getting enough or either - you can give them a balanced fertilizer once a year in the spring and they need 2" of water a week, but are rather drought tolerant.

It is okay to prune back and shape up your rose of sharon shrub. Many folks have pruned them back to two or three feet in height just to make them more manageable and then shape prune them as they grow back. Usually the best time to do this pruning is March to early May. I like to do such pruning late March to early April weather permitting. You could buy or have made, a sturdy trellis and tie her back to that. Some pruning to cut down on the load would be recommended.

There are some Rose of Sharon shubs that are considered sterile so that they do not seed, I hear they also do not sucker, at least not llke the others. Those varieties are:Diana White), Helena (white with red eye), Minerva (pale lavender), Aphrodite (pink with red eye) and also mone named Sugar Tip (pale pink and variegated leaves). Check on their growing habits and light needs when considering what will work best for your planting locations.