Oh, yes, it's definitely possible!
I was going to wait to show this, but the time seems ripe! (Pardon the photos. Oxford Grey Ribby doesn't show up too well on the grey blocking board.)
I knit each of the pieces (I knit both sleeves and both fronts simultaneously) until I got to the armhole decreases. I put each of those on waste yarn (those are the bits of yellow you see), slipped all five pieces onto one 32" needle, and knit across. In this first "join row" I knit two stitches together at each of the "joins," then, purling back, I purled two stitches together at each of the joins, so that now I have a marker between each of the pieces. I figured I needed to do this to "eat up" the selvedge stitches I wasn't going to need. To compensate for their absence, on the decrease rows I simply K2Tog and SSK, without the four knit stitches in between. It's a bit different from the original design, but it's not looking too bad. Here's some detail:
Remember that this hasn't been blocked, so be generous! I decided to try it this way because I hate to sew seams, especially raglan, and because I wanted the collar stitches to be "live" rather than have to pick up bound off stitches. When I finish knitting, I'll graft/kitchener the underarm stitches and seam the sleeves and side seams. Trying it this way (I have to give credit to Claudia who, I believe, did something similar on her very clever O'Ribby) was a bit of a challenge but it's been pretty fun. One of the things I learned is that Peruvian Highland "spit grafts" really well. This is a Meg Swansen trick that allows you to join new yarn without having ends (which are fine if you can incorporate them into the seams, but I didn't want any at either of my front edges.) You strip back about 3" of the one strand of the old skein, and 2" of one strand of the new skein, spit on one palm (or moisten with a sponge if you are delicate), and rub the two ends together briskly to fuse the wool. Voila! One continuous strand.
I'll check back in when I've finished and let you see how it worked out.