No. If you want to use the option of exporting prices and room availability (from BedBooking to Booking.com) you should configure the restriction in the BedBooking price list.
If you don't configure restrictions in the BedBooking price list, the restrictions will also not appear in the Booking.com price list.
The price configuration in BedBooking overwrites the price configuration in Booking.com. If no restrictions have been make in the BedBooking prices, no restrictions will appear for BedBooking prices.