That is a tough one. I do a lot of name research for our clansmen so I gave it a go.
The name Pollard appears to be almost entirely early English. One origin theory was a variation of the the medieval forename Paul (Poll) and Hard meaning brave or strong.
Here is a distribution map of the UK from the 1881 census. As you can see it is almost non existent in Scotland.

http://gbnames.publicprofiler.org/Ma...y=GB&type=name

This is not to say that they weren't there at all- just very few of them.

Good luck
CTB