Wow, that was so easy! Thanks for the tip.
Took about 30 seconds for a 36 page document with 3 layers to check per link.
Had planned to use a list when everything was working. Here's the final:
tell application "Adobe InDesign CC 2014"
# With which document are we working?
set theDocName to "My Indesign Document.indd"
# Create a list of layer names to check
set theLayersList to {"My Layer 1", "My Layer 2", "My Layer 3"}
# Which layer do we want to be visible?
set theDesiredLayer to item 2 of theLayersList
######################
# No need to edit below... #
######################
# Create an object of all document links in the chosen document
set theDocLinks to links of document named theDocName
# Cycle through the links
repeat with i in theDocLinks
# Create an object of all the graphic layer names of the current link
set theGraphicLayers to name of graphic layers of graphic layer options of parent of i
# Cycle through the layers
repeat with j from 1 to count theGraphicLayers
# Set the current layer name
set theCurLayer to item j of theGraphicLayers
# Is this a layer to check?
if theCurLayer is in theLayersList then
# Is it the layer I wish to be visible?
if theCurLayer is theDesiredLayer then
# YES - Set visibility to true
set current visibility of graphic layer j of graphic layer options of parent of i to true
else
# NO - set visibility to false
set current visibility of graphic layer j of graphic layer options of parent of i to false
end if
end if
end repeat
end repeat
end tell