Yes, correctly tagged images helps the overall searchability of your post and content.  Suppose you are writing about a market update about a specific neighborhood and took some pictures of the neighborhood park to include in your post, if you tagged the park photo/image properly the image would also be indexed in Google Image searches.  Although ranking for the search term is just like ranking for regular search – it takes time to rank and as your site builds credibility you should start to show up higher in the SERPs.

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Furthermore, the filename of the image should include keywords that describe the image.   Make the description relevant to the image and do not stuff it arbitrarily with keywords otherwise it could be considered spam.  To add an ALT image to an image, there are a couple of methods.

(1)Manual –  Use this tag format

<img src=”http://mydomain.com/path-to-image” alt=“photo-description-here” width=”75? height=”100?/>

TIP:  Hyphens are better for SEO purposes and should be used to separate words instead of underscores

Use this “Palo-Alto-Park” instead of “Palo_Alto_Park”

(2)Using WordPress’s built in image tools

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(A)After you have uploaded your image, give your image a descriptive title separated by hyphens
(B)Provide an alternate text which would be shown when the user hovers over the image.  This can be the same description in the previous title box.
(C)Add an image caption.  The image caption can use the same description in the title box if designed correctly.  This would make it easier to work with and consistent.
(D)Add an image description.  This description can be longer than the image title.

The combination of all of this tagging should be sufficient for the searchability of your image.