There are persistent reports that the Templar Order, as such, persisted in Scotland for perhaps several hundred years after it was suppressed by the Church.  In researching this, I got interested in the historical Templars and spent some time learning the established facts about them.  By modern Politically Correct standards they probably don't come off too well; the Crusades can be seen as European aggression against Moslems.  It's worth considering that the Moslems themselves had conquered the territory during the decline of the Holy Roman Empire.  In the context of their time, the Templars seem in many ways admirable.  Most of them appear to have been honestly devout and to have made some real sacrifices for their beliefs.  In their time, the distinction between the nobility and the clergy was very pronounced, in particular the prohibition against the clergy using weapons or shedding blood (when the Church wanted to torture or kill, they delegated the work to secular authorities).  The Templars were often considered, and often considered themselves, inferior to the more traditional orders.  Undoubtedly, they often failed their ideals, especially after they became rich and politically powerful - they were, after all,  human.  Just as certainly, most of them had a monastic way of life with few material comforts and a great deal of hardship and danger.  Most of the charges brought against them at the instigation of Philip IV were obviously either false or gross exaggerations which were widely discounted outside of France.
The history of the Templars in Scotland after the suppression of the Order is less certain.  Robert the Bruce became King in 1314, a year after Jacques De Molay was burnt at the stake.  Robert had already been excommunicated for killing "Red" Comyn on sacred ground, and the Scottish nation interdicted for accepting him as their king.  The Scots certainly had no reason to honor the Bull of Pope Clement V ordering all Christian rulers to arrest the Templars; on the contrary, they would have welcomed the help of such a trained and seasoned fighting force at Bannockburn and beyond.  Of the many Templars already in Scotland, only two were ever arrested, and word would surely have spread that the nation offered a refuge from the persecutions on the European continent.  Whether those seeking refuge actually brought with them material treasures or objects  of spiritual significance is less certain - very likely they would have done so if possible.  Reports of the persistence of the Order per se in Scotland are anecdotal, but there are an impressive number of them.

Credits:
My main source of information on the historic Templars is The Knights Templar by Stephen Howarth, 1982 (Barnes & Noble Books ed., 1993).  This is a very comprehensive and readable survey of the entire subject, including the period from about 1150 to 1250 that many descriptions (including mine) brush over.  I have also used The Knights Templar and Their Myth by Peter Partner, 1992 (Destiny Books ed.).  Dr. Partner's book has a good but briefer summary of the historic Templars; however his primary focus is on "debunking" the esoteric elements of their tradition and its later claimants.  The map of the Holy land came from U of Texas Library Online, PCL Map Collection, a wonderful archive of maps, which are in the public domain.  There are also a great many web sites relating to the Order.  Two that I found very useful are Knights Templar History, which has a timeline summary, and Paul Halsall/Fordham University: Medieval Sourcebook: Foundation of the Order of Knights Templar, part of a much larger collection of historical material.  There is a lot of interesting, mainly anecdotal,  material on the history of the Templars after the suppression on the Order on European Knights Templar Heritage site.  Finally, I would like to thank my friend Deborah MacGillivray Rogers for all her help and material.  Deborah has her own web page now, PictLadyCat's Scottish History Pages, and it's an excellent resource on Scottish history.