Can I run a pyspark jupyter notebook in cluster deploy mode?

You cannot use cluster mode with PySpark at all:

Currently, standalone mode does not support cluster mode for Python applications.

and even if you could cluster mode is not applicable in interactive environment:

case (_, CLUSTER) if isShell(args.primaryResource) =>
  error("Cluster deploy mode is not applicable to Spark shells.")
case (_, CLUSTER) if isSqlShell(args.mainClass) =>
  error("Cluster deploy mode is not applicable to Spark SQL shell.")