As someone based south of the border, this is how I see it.
The current sleeper is a loss maker supported by Holyrood. I can see good reasons for continuing to support it, but surely the subsidy required for an international service would be far higher, and that would be on top of the existing subsidy to the domestic sleeper.
The London > major Scottish destinations market is huge in comparison to the Paris, Brussles (which are the two most likely southern end points) market. I dont know what proportion of journeys the sleeper contributes, but even if you just count rail journeys London > Scotland it must be small, so a similar percentage of Continent > Scotland journeys would result in a lot of fresh air being carried unless fares were budget airline low, which in turn would mean an even bigger subsidy.
Overnight sleeper to London followed by Eurostar is probably almost as quick if you dont want to fly.
Border formalities for 1 or 2 trains per day would need to be set up in potentially multiple Scottish locations for maybe 1 return service each day, and if you used the current model and did both sets of formatilies at the start of the journey you would need a French contingent at the Scottish end, which quite rightly the French would charge for.
This is before you get into the technical side, rolling stock, signalling, traction.
Why are they even 'throwing money' at it?