The short answer to your question is "No" or at least "Not Necessarily."
The medium length answer is that what these results show is that the tester's dna matches people who Ancestry class as "Scottish." Ancestry consider their comparison group as Scottish based on their genealogy placing them (and their ancestors) in Scotland for several generations.
The long answer is that Ancestry (and every other genealogical DNA testing company) simply try to match your DNA sample with other people who have "known" association with a particular location.
Contrary to popular belief, there is no such thing as Scots, Irish, Norse or anything else DNA.
What there are, and what DNA testing companies rely on, are similar clusters of DNA segments (called SNPs) which are common in populations around the world. Where a particular SNP is identified with a particular location (because it appears in the DNA of a relatively high number of people whose genealogy is associated with that location over several generations) then it serves as a marker that your ancestors MAY have lived in that location at some stage. The more SNPs associated with a particular region, the higher the %age it produces in it's final estimate.
The thing to remember is that Scotland and England have both been subject to major migrations, invasions, and simple movement of people in search of work etc.
To give an example My own family are pretty much constantly from the mining villages of Lanarkshire and West Lothian on my mother's side, and farmers in Ayrshire and Argyll on my father's right back to the late 1600s. One couple came across from Ireland - my first brick wall, sadly - but otherwise it's all Scottish - which in my case matches the ethnicity estimate surprisingly well. However, given that both sides of my family lived near the coasts, it seems highly unlikely that no where in my line is there someone who married someone of Norse descent - but that doesn't show as "Norse" dna, because it's probably true of almost everyone in Scotland.
The other point to remember is that estimates of ethnicity based on current dna are less science and more guesswork with a bit of probability thrown in.
