You will need the solid mounts if you weld in the sub connectors. Yes, on a street car the solid mounts transfer a lot more road/mechanical noise to the occupants.
But you must connect the subs if you plan on any big h-power and good traction drag racing. My big block 70 with 11" slicks, 4:56 rear, broke the body where the quarter panel is leaded to the roof, high up. This was when the car was less than a year old.