The pins should help it center, but the large pad under the chip will do
pretty much nothing.
Give it a little thought. The centering works by surface tension. A
pin is typically not much different in size to the footprint. If
movement significantly changes the shape of the solder at the edges, it
will create a force from the imbalance of the two sides. But if you
extend the footprint pad far beyond the pin (or in this case the large
pad under the chip) the change in shape will be very small for a small
movement and there will be very little force generated.
What John is saying makes sense. Use your large footprint pad, but add
solder mask to define the pad area under the chip, then leave openings
in the solder mask *outside* of the chip to lay your soldering irons.
This will give you the proper pad area under the chip which will make
the assembly house happy and give you areas to heat the thermal pad with
soldering irons.