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Ah, sorry, I meant can the remaining loft above your loft conversion still access the outside world without going via the eaves storage space?
But perhaps it's immediately the ~25mm cavity below your roof felt which joins the eaves storage space? Essentially you need to allow the outside world to get to the cavity beneath your roof felt in some form, so making the eaves storage space more airtight might not be the best approach unless the roof is already separately vented to the cavity underneath and doesn't rely on the eaves at all.
Is your loft ventilated to the outside world without going via the eaves? If so, plugging the gaps might make sense. Essentially the eave is a 'cold loft' though, right? If so you'd get more returns further isolating it from the loft conversion and rooms below.