Answer: Yes and No.
No: Respondent's Project Calendar
Each Calendar is project-specific, meaning that it's not shared across your other projects. Let's say you have two projects running concurrently, you should set up your Availability to avoid overlap.
Project A: Availability on Monday, Tuesday and Wednesday
Project B: Availability on Thursday and Friday
Yes: Use a Connected Calendar
Setting up your availability in this way can be tedious, especially if you're running multiple projects at a time. In this case, the best way to centralize your scheduling and avoid appointment conflicts across projects is to integrate your Google or Outlook calendar. Integrating your Google or Outlook calendar will allow Respondent to check for conflicts and add bookings directly to your personal calendar.