That's a very good suggestion, Paul, and how I mixed up mortar on a recent trip to Spain where I obviously didn't have access to my own kit. The only thing I'd say is that you'll need the purpose made machine for this, with two handles, and not the beater-thingy which fits in a drill. The latter wouldn't be man enough for mortar. I can imagine either hiring the tool, or buying it on ebay then selling it on when the job is done.
Ten bricks an hour might be realistic for building up corners using a spirit level, but "running in" with a line even a beginner will manage more than 40 bricks an hour.
Tom, there are two ways you can approach the brick laying: 1/ building corners, then the following day "running in" using a line pulled tight between the corners: or, 2/using profiles. These are essentially a post marked out at 75mm intervals (to the correct heights) set near the corners, between which you tension your line. They take more time to make (from battens/ off-cuts) and set up to the right line and height, but once they are in place you're off and running with the easiest form of brick-laying, "running in" with only a line to tell you where to place the brick. I much prefer the latter, as using a spirit level to plumb vertical when there are only two bricks, and they are both still moving about, is an annoying faff.
Oh, and cleaning a mixer is no hassle. Scrape it out when you take out you last load of mortar, spray it down with the hose, chuck in some broken bricks, and leave it running for quarter of an hour. Turn it out, spray down again quickly. The biggest argument against using a mixer (if there is one) is that the batch size might be too big for your first go at brick laying.