Why is DNA testing important to a family like ours and of what use will it be to us?
To prove or disprove that we all share a common ancestor.
To prove or disprove that a variant spelling of our surname is linked e.g. e.g. Strachan, Strawn, Strahan, Straughan, etc.
In the event that ancestors adopted the surname of the leader of the community or in honour of the person they worked for, we can establish the various groups who do share a common ancestor. The advantage here is that one or two members of the group might be further advanced in their research than you and can therefore indicate in which geographical area you should continue your search.
To indicate where mistakes might have been made in family trees when it is found that certain descendants do not share the same or very similar Y-chromosome data.