Does number of rows affect Update Statistics performance if you are sampling with n rows?
Update statistics is a single threaded task (You can run multiple instances of it in parallell though) so duration of the statistics run will be correlated with the number of records the task has to scan in order to build the statistics and selecting the rows to sample.

Even if you are only sampling a fixed number of rows the population you are sampling from is larger therefore the scan will be more time consuming.

There are some interesting details about effects and use of tempdb in statistics scanning in Erin Stellato's post about statistics but almost all you want to know is contained in this Robert Sheldon's article