Yes, there is a connection of course, just not the connection he is looking for.
1 year = 365.242199~ days
That is a correlation, just not one that is expressed in nice round numbers. It does not follow that this is, therefore, any evidence of randomness, unless one doesn’t understand the everpresent nature of irrational numbers in the universe.
1 Circumference = 3.1415927~ diameters
That is not a nice round number correlation either, yet who would argue that the existence of circles is evidence of randomness vs design?
I’m on the side of design.
And if the ratio between orbital and rotational periods were the same for every planet the way pi is constant for every circle you’d have a valid point.