Obviously, yes, the Scotland-England border would become an EU border. It is realistic to expect that border to be dealt with precisely the same way as the north-south Irish border. In any case, that is an EU matter and would/will be designed and implemented by the EU - Scotland's awareness of it would be greater than in other EU countries as it is on the edge of Scotland.
Brexit has led to such things (Ireland and potentially Scotland)and, one way or other, it would/will be dealt with without much delay. The Irish version is a particularly sensitive one due to the history involved (past and up to the present), Scotland's would/will not involve that aspect and in that sense may be easier to implement. Scotland's would/will be a relatively straight forward copy of the rest, the way things are going perhaps not unlike the border between Finland and Russia rather than Greece and Turkey (there are far more sets of agreements in place between Turkey and the EU) - how often do people in France, Germany, Netherlands, etc. give thought to how they work while Finns, Greeks, etc. are no doubt more familiar with the practicalities ?