Answer: Apparently, yes it could. I found a published report from the Minnesota Water Garden Society
indicating that yes, it could puncture a liner. This is not too surprising since it is also reported to grow through pavement. If you grow this plant it should always be in a solid bottomed container and periodically thinned to make sure it does not escape over the lip of the container -- or pierce it and escape that way. This plant grows quickly and is truly invasive, even when planted in the ground. Once established, it is very difficult to get rid of it where it is unwanted. I would suggest you proceed with caution.
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