Nurseries need to respect parenting wishes as far as possible. As using cloth is becoming more popular, the response is more likely to be 'yes' or 'yes, if you show us what to do', rather than an outright no.
We send bumgenius or coolababy pockets and they are fine with them. They even rinse the really stinky ones for us. They have lost 2 in 2.5 years, which is sad, but at least they were basics.
I wouldn't send anything posh or expensive, and it would be easier if it was just a single sort (ie poppers pockets, or aplix 2 parters) and be prepared to show them what to do.
Go for it!