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I kind of agree with buckworks, by changing it something like visit the REAL blue widgit site as mysite.com would probably be very constructive to you. I would think twice before purchasing some thing from a site that was doing that kind of advertising. I would be more likly to think they where reselling from you so I would go to you.
It certainly can lead to your images being stolen more often, and either linked off your server or just copied and reused.
OTOH, it may generate some useful traffic. Google image search always gives the opportunity to open the whole page, and as a searcher I usually do if I find something of interest. If you sell widgets, and someone does an image search on "widget", it stands to reason they might be interested in your product. Sure, they could be a competitor looking for a widget picture to rip off, or they could be a widget collector. Who knows? Personally, I usually give my images logical names related to the content. I may not get a ton of business via image searches, but why not try for that little bit extra?
I had some fun the other day with someone who ripped off an icon from one site, and even linked it from my server. (If you are going to steal an image, don't steal my bandwidth, too!) I noticed that the thief hadn't included height & width attributes, so I replaced the icon-sized image with a page-width graphic noting that this web site steals graphics... They cleaned up their act pretty quickly. ;)
you can prevent hotlinking of images with .htaccess
I like image traffic - although my industry might be more image related than most - it has made sales for me.
You can't be afraid of people finding you and stealing your stuff. That is what Search Engines are for.
Personally - I think the alt tag and surrounding text is much more important than the image itself.
But I do sometimes put the keyword in the image.
Hotlinking has not been a major issue, and where it has occured, I've "fixed" it. I love the traffic I get from image searches: nice conversions too! Make everything count, name those images!