How to tell if a tif file contains an embedded ICC profile?

Yes, using imfinfo as follows.

fileData = 'corn.tif'; % Example matlab file that doesn't have an ICC profile embedded
a = imfinfo(fileData); % Get info about the file
isIccEmbedded = isfield(a, 'ICCProfileOffset'); 
% Since no ICC profile is embedded, this is false

% Go through Step 5 at the following website to create an example tif
% with an ICC profile embedded,
% https://blogs.mathworks.com/steve/2009/10/20/embedding-an-icc-profile-into-a-tiff-file/
fileData = 'peppers.tif';
a = imfinfo(fileData); % Get info about the file
isIccEmbedded = isfield(a, 'ICCProfileOffset'); 
% Since an ICC profile is embedded, this is true

I saw this mentioned in the iccread help file and thought an example would be useful.