I have a TTWeights 600gm peripheral ring which I use with a TTWeights 800gm Stainless Superweight. It's not on a DD but it is on a table that supports a very heavy platter. I can't comment on any speed differences but can say that startup will be slower/harder on the motor. Once it's up to speed there should be no issue as the ring actually improves inertia.
Between the ring and center weight, a typical record is flattened out almost completely. Records that are edge warped from heat are not flattened completely but well enough they may be playable w/o skipping. Whether the cartridge has enough room to clear the edge of the ring depends on the make - I have one that will not clear the lip but it also won't track heavily warped records. Cartridges with a small footprint and a VTA of at least 20 degrees should be ok.
Most significant about the ring is the change in sound it makes at the beginning of the record. You might not be aware of it but the sound of a record changes from beginning to end, especially if you already use a spindle clamp/weight. This is because the damping of the vinyl attributable to the mat is greater near the label than it is at the edge, especially on warped records. By clamping the edge of the record down, this inequity is reduced allowing the record to be damped evenly across the surface, ensuring the tone doesn't change during playback.
Apart from that, the ring offers many of the attributes of a spindle clamp/weight; better dynamics, tighter bass, lower noise floor, etc. Flattening the record is the last reason I use it.