It depends. If you are simply doing a tube journey from one tube station to Euston tube, and your only National Rail ticket is your Euston-Glasgow ticket, then no. Although, if there is major disruption on the tube, you may be able to persuade the Euston ticket office to authorise travel on a later Euston-Glasgow train. (If this is your situation, next time consider buying an Advance from your London travelcard zone to Glasgow: they are normally the price of the Euston-Glasgow advance with an add-on for the single tube trip.)
If your tube journey is part of a through journey that started on National Rail, and was fully ticketed through to Euston (e.g. Woking to London Zone 1, not merely Woking to London Terminals), then having split your tickets should not prevent the "guarantee" applying so long as you allowed the required minimum time for the cross-London tube transfer.
And some on this forum would say that your Euston-Glasgow ticket, combined with e.g. a Woking-London Terminals ticket, should be enough (if you left the minimum time for the tube transfer from Waterloo or wherever).