I would like to know if Process Builder is available in Professional Edition, also, what happen if we attempt to install a managed package that contains Process Builder as dependency?
Lightning Process Builder is even available in Professional Edition:
Available in: both Salesforce Classic and Lightning Experience
Available in: Professional, Enterprise, Performance, Unlimited, and Developer Editions
While many of the other features for automation are not available in Professional Edition, they're finally giving Professional Edition users some ability to perform automation.
I might be responding to this question a bit Late but,
What sfdcFox said is correct however, I faced an issue with Professional edition while installing a package with ProicessBuilder. My Processbuilder has ACTION TYPE set to APEX because I am using a @future method to make API calls when the processBuilder is triggered. It resulted me to failing the installation as ACTION TYPE set to APEX are not compatible in Professional Edition. Please mind that and other ACTION TYPEs might work without any issues. Please go through the documentation depending on your requirement.