Not quite.
From the exception of Tertiary volcanics like Skye, all things NW of the Highland Boundary Fault (ie Stonehaven, Crieff, Bute) were part of the ancient continent Laurentia which present day North America and Greenland were also part of. The Grampian block SE of Loch Ness (the Great Glen Fault) were shallow marine sediments on the Laurentian (i.e. 'North American' plate) continetal shelf and lateral equivalents to the NW Highlands. The Midland Valley terrane however was a separate volcanic island arc system like Japan which later crashed into it as the Iapetus ocean between Avalonia (England) closed. The final stage involved England on the other side smashing into us and this is what triggered most of the granite formation within the 'Caledonide' mountains, formerly the size of the Himalayas but we're now just seeing the eroded roots of it. These granites were formed ~350 million years before the Atlantic even started spreading.
Iceland is a very recent part of the Atlantic Ridge volcanics splitting up what was previously the amalgamation of these continents with a few more added on. Technically Iceland isn't on any continent as it's on thinner, basaltic Oceanic Crust, not thick continental. Scotland has always been on this side of the Atlantic. We haven't sailed across it, it's simply split us apart from North America. Skye, Mull etc are just two 'ancient' Icelandic style volcanic centres from when this ocean spreading kicked off.
Additionally, only the SE of England has much chalk, most of it's sandstone, limestone with some lavas in the lake District etc. However, chalk would probably have covered the British Isles (including Scotland) but most of it's been eroded away. Most of England's water comes from underground aquifers and hence the limestones of northern England make the water 'hard' and shyte. Most of Scotland's comes straight off the mountain and stored on impermeable hard rock, e.g. Loch Katrine.
Sorry for that, but I felt it needed addressed.