What will I see?  I point a standard down scan transducer 45 degrees down and out in front of the boat and have it on a motor drive so it moves back and forth at 45 degrees.  If I slowly move down the lake on speed 2 trolling motor...will I locate fish in front of the boat?  See arcs?

it will be a garbled mess on the screen.  The processing unit won't be able to put the picture together properly.  it will think you're in 60-100' of water depending how deep you are.  Lots have tried, none have been successful.  If you're looking for a poor man's live imaging just get the cheaper fisheye unit.

I agree it would not work well.  I haven’t tried it but my best guess is if you spent thousands of hours practicing and learning to interpret what you see on screen you might occasionally be able to identify a fish.  
 

If the fish was high enough in the water column not to be masked by the extra wide bottom band,  I think it would appear as an arch as the transducer is rotated.

Funny you ask this, as I was just thinking the same thing last night. However, my thoughts are if it’s looking “out”, with no bottom in sight, it’s hard to get a sonar return I would assume…

It wouldn’t work well with down scan due to the beam characteristics - wide but extremely narrow in thickness. You’d likely get nothing but dots and dashes, if that. But if you had a flasher or a traditional 2d sonar, especially with a puck type transducer, you can get it to work, though it won’t be quite the same as modern live imaging units…but you’ll see stuff ahead of you, including fish, once you get everything dialed in.
 

Lowrance diagrammed exactly how to do this, albeit through the ice, in their 1972 Lo-K-Tor manual, and on my 2002 Triton I bought new, I had the marine dealership rig up my bow unit (flasher) to do this exact thing. I refer to it as FLS - forward “leaning” sonar - lol. It worked great, and almost nobody did it l, or thought about doing it, back then. I got the idea after fishing with a guide on Table Rock the previous year who had adapted an LCR (2d) version of this. I was impressed enough after seeing it to take it one step further, rigging it up so I could scan ahead of the boat by putting the puck on the trolling motor head. To this day, we’re the only two people I know of who ever had our boat electronic units set up that way.
 

I don't know about DI, but I've been scanning under docs with SI on a TM for well over a decade. You have to move the the head slowly and smoothly to get an image that is somewhat readable.