I think this is a great question to ponder.

Firstly I think you need to look at the fact that Queen Mary would have been very aware of the cost of losing a war or the social disruption it could cause for those on the throne. With her purchases of jewels in the 1920's she would also have known of the importance of jewellery "in keeping you afloat" in exile (permanent or otherwise) and also of the fate of Queen Marie of Romania's jewels or as I believe Empress Zita's who I believe went into exile with virtually nothing. The number of Romanov's who didn't keep their jewels close in the revolution and lost them would also have been very front and centre. I would suspect she knew of Goebbels sticky fingers as well.

There is also though the interesting question in the accuracy of a suitcase full of tiara's. With the amount of tiara's Queen Mary had, which would require a trunk to travel with, combined with the ease of flight it would have been impractical, and would not of have gone with something custom made for a WWII get away she probably she would have used an existing travelling jewellery suitcase. This would probably have had various compartments for either the existing boxes or for tiara's, necklaces etc to have been put into to avoid them damaging each other in transit. I doubt this would, as mentioned, have housed the entire collection without being too big for swift and convenient movement.

So I would suspect that jewellery would also have been split into the other suitcases and items like the Cullinan brooch good to go into a pocket. A tiara whist on top of the head isn't necessarily top of the value for jewellery items.

I think other aspects to consider are what would have been the getaway route? The RF would mostly likely have headed north (assuming invasion was from the south, east or both) and I doubt QM would have willingly agreed to leave the UK on immediate invasion unless tasked to do so with the instruction to accompany the princesses, so I suspect a fall back prior to any evacuation would be Balmoral. In fact during the cold war it was from Balmoral aboard the Britannia that the RF would leave the UK in result of a nuclear war. So there may have been a jewellery repository in Balmoral in case jewellery was lost or had to be sacrificed due to the many circumstances that could arise from a wartime evacuation.

I've also always thought that the RF may have sent jewellery away to perhaps Australia, NZ (again always the fall back country due to it's remoteness) when the likely hood of war was building up or even the USA in order to cover for any financial contingencies in result of exile.

When it came to clothes QM could have sold a medium size brooch and not had to think about her wardrobe for a few years so I'd imagine jewels trumped even the wardrobe dignity.

So to conclude I think QM had jewellery that was good to go and there's an overall very believable factuality and accuracy to the article. So in answer I'd say she probably had very nearly the majority of her jewellery on her.