Inns of Court Scholarship - A career springboard?Watch
From your experience, if someone doesn't have a Scholarship for the BPTC, his/her chances for getting at least the interview for pupillage are lowered in contrast to those who already possess one?
The question, as with many 'are my chances of securing pupillage better with 'x'/worse without 'x' on my application form?' questions, is too binary and misunderstands the way in which applications are sifted. A BPTC scholarship is a good thing to have on your application form, and it's better to have one than not, but it's not the case that you'll gain or lose 'marks' specifically because you do or do not have such a scholarship. Different sets will assess applications differently, but the assessments will invariably be more holistic than that, and candidates are rarely directly compared during the sift.
A good application form broadly speaking is what makes you stand out. So a BPTC scholarship might help you to do that. But if you don't have one, it may be that you have a different scholarship, or that you've won some sort of prize, or that you've got a First, or some fantastic work experience, or a hundred other ways that you could stand out. Basically the advice is that you shouldn't get too hung up on one particular element of your application, the one exception to that being if you fail to achieve what would be considered a bare minimum (e.g. you get a 2:2, or a Competent on the BPTC). You should be looking to improve your application constantly as part of an ongoing process, and there are a lot of different ways that you can do that. One particular element being present or absent from your application is unlikely to make or break anything.
It is certainly possible to get pupillage without a scholarship from an Inn. People who get pupillage on the GDL often do not have BPTC Inn scholarships at the time they write their paper applications and go to interviews. However, there is often a 'Scholarships / Prizes / Awards' section on a pupillage application form. It is ideal if, rather than leaving it blank, you have something to write there, e.g. winning or placing in an essay competition.