short answer is yes. long answer is...make sure your background layer has an alpha channel by clicking on it in the layers dialog to make that layer the active layer. If add alpha channel is greyed out, then it does, if not then click on add alpha channel. Then, in the layer dialog, you can use the opacity slider on that layer and lower the opacity. you use right click to bring up choices in the layer dialog.

Another thing to note, a layer with an alpha channel will be shown as bold in the layers dockable dialog box. This is a quick way to check to see what layers have alpha layers and what ones do not.

That's strange. On mine, when I add an alpha channel the word background goes from thick (bold) to thin. When I remove alpha channel, it turns bold.

oops. I must have said it backwards. Sorry, should have checked my source first. I will correct the post to say what it should say.

LOL, I just thought maybe I had the weird one cuz nothing else seems to be going my way with here Gimp lately. Anyway, one is bold and one is not.

Foreground to transparent gradients can work well for this also.
Depends on what you want i guess.

Not to mention layer masks.

I have never tried this, but is it possible to use a foreground to transparent gradient multiple times on one mask (to get a nice feathered edge around the foreground image). I imagine you would use a white full opacity mask?

it is indeed possible, I do it all the time for creating vignette effects. Yes, you would use a white layer mask and use a black to transparent gradient around the edges. The layer would be filled with black (or whatever works for you) and the layer mode would be set to overlay.