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Google will certainly offer Alt Text, bolded in a snippet, if that's a relevant match for your search.
Besides, it's extremely good practice for accessibility reasons, to use Alt Text the way it was intended.
Then, you'll have an accessible site that's properly indexed.
DerekH
This is easy to show, by taking an un-linked image (maybe on your own site) and search for the alt-text.
And Google will not present the alt-text of un-linked images either.
You can test this by searching for text that surround your un-linked image - and then watch the Google snippets.
IMHO Google uses Alt tags without link text but doesn't give is much value.
Every image should have some sort of alt attribute text, as the text of that is used by screen readers for disabled surfers, and for people with non-visual browsers, or where image loading is switched off, or the image fails to load.