Do large animals experience a meaningful delay when moving their most distant appendages?
Yes, larger animals do experience larger delays in movement.

There have been studies of size difference vs sensorimotor delays in terrestrial mammals, https://www.ncbi.nlm.nih.gov/pubmed/30158304


That graph is for innate reflexes of a needle to the hind versus a kick-time. Perhaps no one dared to prick a blue whale.

Elephant vs shrew, heartbeat of 30 vs 1500 BPM, elephant 50 times slower than the shrew. Larger animals compensate with a better ability to predict physics and kinematics using their larger brain. 

There are other kinds of movements which have more complex neural pathways that the graphs of pin-prick reflexes, that are even slower compared to size, you can study the physiology of eye to hand response in humans which varies from 120ms to 270ms for different humans. 

It does have an effect on survival for example with a mongoose versus a snake, the mongoose has more versatile and faster reactions. 


There are also weasel attack videos on the web.
some graphs here