No, it won't. Chara's crunchy feel is due to lime. Chara absorbs lime. It needs it to grow. So, even though you aren't actually feeding the plant with lime, you give it some of what it needs with lime.
Remember what chara looks like when it sits out of the water for a few days? It turns white, and disintegrates. Pull a chunk of the stuff out on the shore, give it a few days, then pick it up. The white is lime.
Also, you may want to know that chara is an algae. That's important to know to choose the best course of treatment, should that be your choice.

Teach a man to grow fish...
He can teach to catch fish...