Yes. Ribonucleases (RNAses) break down the spliced RNA strands back into mononucleotides, and these building blocks can be reused.
They will be broken down into nucleotide monophosphates, so they will have to be re-phosphorylated to triphosphates before they can be reused for transcription.
Here are a couple of reasonable reviews of the mechanisms:
Another use for a spliced out intronic piece of RNA is as noncoding RNA. Here's an example which include pre-mRNA also transcribing microRNAs.
U3 RNA with its proteins forming a complex is localized at nucleolar. The box C'/D motif in U3 snRNA is responsible for this localization. Therefore U3 snRNA does not have a chance to go to mRNA transcription active sites. Instead, U3 snRNP play important roles in ribosomal-RNA processing.
Because of necleolar localization, U3 snRNA is called U3 snoRNA ...