Can AWS Glue crawlers crawl parquet files to iceberg type table?

The crawler doesn't do any conversion on the data, it registers what you have there.
So if you just have parquet files and not an Iceberg table, the crawler cannot do that. What the crawler can do is register an Iceberg table in S3 you already have.
Iceberg has utilities to create a table based on existing files, then you can ask the crawler to register it:
https://iceberg.apache.org/docs/latest/spark-procedures/#table-migration