It is possible to call API requests to Power Automate and edit cloud flows via PAD, but there is no direct integration to that.
Also, if you want to use Desktop flows with Cloud flows, you actually need a "Power Automate per user plan with Attended RPA" which comes at a cost of around 40 USD/month. PAD is only free for Windows 10/11 as long as you don't wish to use it with Cloud.
The 15 USD/month subscription will only allow you to use Cloud flows, but will not enable any communication between Cloud flows and PAD, if you are using the free version of PAD.