Not sure, full disclosure, about the full scope of your question. Details matter.
However will go out on a limb so to speak and answer "perhaps". The unmanaged switch will/should work.
But only to some certain unknown extent. The reason being that going from managed to unmanaged may result in some performance hit on your network.
There should be some reason(s) for have a managed switch to begin with.
Check the following link:
https://community.fs.com/blog/managed-vs-unmanaged-switch-which-one-can-satisfy-your-real-need.html
Per the link look at the differences between managed and unmanaged.
Determine if the existing managed switch is really doing anything for your network and operational environment.
What requirements exist that, if any, support the need for a managed switch?
Are you able to provide more details about your environment? Very sure that someone here can provide further insight or otherwise address the matter in more detail.