I don't think there is any way in vanilla MEL to query that information. ShelfLayouts are a custom compound control type, so the only things you can really query are the parameters exposed to the `shelfLayout` command. If it was a regular `scrollLayout` you could make an informed guess that the scrollBar was visible by querying the width of the scrollLayout and the width of it's child layout and comparing the two to see how much difference there was, but I'm not even sure that's guaranteed to work 100%.
You can, however, do this relatively trivially in Python, by querying the underlying Qt Widgets, but it does get quite involved if you're not familiar with Python/Qt/Maya API 😅
But if you did want to stray away from the comfort of MEL, it is possible, for example (tested on Maya 2023, probably won't work on 2025 without editing, as that uses PySide6):
from maya import mel
from maya import cmds
from maya.OpenMayaUI import MQtUtil
from PySide2.QtWidgets import QWidget
from shiboken2 import wrapInstance
def isCurrentShelfScrollbarVisible():
"""Returns True if the scrollbar is visible on the CURRENT shelf."""
# get the main Shelf Layout using MEL vars
layout = mel.eval("string $nul = $gShelfTopLevel;")
# get the current shelf
shelf = cmds.shelfTabLayout(layout, q=True, selectTab=True)
# get the pointer to the control object
ctrlPtr = MQtUtil.findControl(shelf)
# wrap it into a literal QWidget
wrapInstance(int(ctrlPtr), QWidget)
# Get the widget's children (we're looking for QScrollArea)
childWidgets = widget.children()
# the QScrollArea is the second item (really we should check this)
scroll = childWidgets[1]
# return whether it's verical scrollbar is visible or not
return scroll.verticalScrollBar().isVisible()
and you could then call this from MEL like so:
int $shelfScrollbarVis = `python("isCurrentShelfScrollbarVisible()")`;
