Yes, you should.
While there are parts of your scenario that we don't know, there are some generalities than can and should be applied based on known formulas and user expectations. One of those is the thumb minimum size.
Take a look at the image below:
here you have scrollbars from lots of different systems across decades. However, you'll notice that with the exception of Apple Lisa, they all share something in common: despite the amount of content you may imagine (since is not shown, but can be deducted) and the technical ad UI approach, the thumb is always at least as high as the scrollbar width.
This is easily proven if you use a native scrollbar in most operating systems: the default will be immediately applied, you have to do nothing. Microsoft says the following:
The minimum sizes for a Thumb control are determined by two system
parameters, VerticalScrollBarButtonHeight and
HorizontalScrollBarThumbWidth. The minimum size for a Thumb control in
a vertical Track is 1/2 * VerticalScrollBarButtonHeight and the
minimum size for a Thumb control in a horizontal Track is 1/2 *
However, you may want an even higher minimum value, for which you have 2 options:
1. Set a fixed height
This will require some calculations, because you'll need to consider the scrollbar, its controls and the new minimum height. So if you set your thumb at 30px height as minimum, then you'll need to make room for this and "fire" the scrollbar 30px earlier. You can see a VB sample implementation document here but it basically means this:
<!-- Set the height of the Thumb.-->
2. Set a variable height
This is what I'd recommend, and there's a calculation for this:
ThumbSize = TrackLength * ViewportSize / (Maximum – Minimum + ViewportSize)
you'll need to specify
ViewportSize property for this
of course in iOS you don't have persistent sidebars, but that's another story. For the purposes of your question, it's enough to say that the thumb height won't visually aid the user since the scrollbar itself is not visible