Q: Can a Desktop PowerPC G3 computer be oriented on its side?

You can orient it any way you want. The main concern should be you don't cover any cooling vents.

If oriented vertically, the desktop model shouldn't be placed on the left side, where the PCI slots are located.  The power supply's cooling fan is on the underside of the drive bay sub-chassis.  It's designed to draw air in through the vent holes on the left side, across the motherboard, and then exhaust the warmed air through the rear of the computer.  For symmetrical styling of the case cover, both sides have vent slots running from front to rear, but the fan's intake is below those slots on the right side.  More air (and it's not the greatest design for effective cooling) is pulled in through the holes on the left side of the chassis wall, located behind those vent slots on the left side of the case.  Cooling a PCI graphics card would also be another reason to keep the computer's left side oriented upward.

Bill,

the cooling issues due to the G3DT design Jeff mentions are exacerbated when you have two hard drives. "Back in the day" when the Beige G3 was fast 'n furious, we always cautioned people with the desktop version about watching temps when the extra bay was occupied. One recommendation was to substitute round ATA/IDE drive cables for the ribbon-type to help air flow. The case design was critical enough with heat issues that the round cable thing actually helped.

So, regardless of orientation, you are starting with a case form factor that has a history of needing to be "babied" to avoid heat problems.

By comparison, the spacious mini-tower model had few cooling issues plus had available mounting points for up to two extra 60MM fans to better cool the PCI array. I wish the DT versions had that flexibility.

You've got a very capably-upgraded G3 desktop.  I think it would be a good idea to block up the right side about an inch or so.  I did that for a Power Mac 6100 that I had, because of its floor-mounted PSU fan that was positioned only ½" above the desk's surface (a terrible design).  The extra height under it enabled the exhausted air to better escape.  I've got both style G3 models and agree with Allan - the mini-tower was far superior in terms of cooling design.  The main problem with sliding the mini-tower into an enclosed compartment (like so many computer desks have) is that its air slots on the left side would be blocked.  Then the desk would need a slight modification, to permit air flow to that side of the computer.  I'm curious as to which EVGA PCI graphics card you installed.  I settled for ATI Radeon 7000s in mine, with a mixture of 32 MB and 64 MB ATI-manufactured cards that I flashed in one of my PCs.

the stock CD drive tray does not have those little tabs that you can pull out to secure an optical disc when mounted vertically.  Some of the replacement optical drive models may have that capability.  have you ever upgraded the internal optical drive?  If you don't have a tray with those extendable disc retainers then you can not load a disc in the vertical orientation, the disc will fall out of the tray.

when I had a G3 desktop with a g4 cpu upgrade and extra hard drives, it would overheat.  I always used external speakers, so I removed the internal speaker and mounted a little Vantec stealth fan in that space to help blow air from the front of the case into the cpu heat sink area, it seemed to help.  The stock G3 cpu might not run as hot.  also, fresh thermal paste between the heat sink and cpu helps keep the heat sink working.

when the speaker is removed, you will create a new air vent, which helps the CPU and hard drives get more cooling air, but it may detract from the original cooling air path through the left side vents over the PCI cards, ie your video card.  Some video cards have their own little fan on the heat sink, but some don't.  It might not cause any problems without another fan, but see how much space you have in there, you might be able to fit a 60 or 80 mm fan, run a splitter from one of the hard drive molex power plugs, but you might not like the extra noise.

also, the hot air is blown out the back through the PSU, make sure that hot air can escape the back of the desk and rise so that it does not get sucked back into the G3 case cool air intake vents. 

HAve you figured out how to write an AppleScript or alias to first mount a CDRom image file, than launch the application?   That would be cool, I have thought about converting some old CDroms to disc images also, good idea.

You may have problems related to the driver that you'll use for the Radeon 7K under Mac OS 9.1.  As I recall, the final pre-OS X ATI driver with Radeon Support (I can't remember the version #) had compatibility problems with anything less than OS 9.2.1/9.2.2.  Under Mac OS 9.1 (and even 8.6), I don't think the installer would run.  Manually placing the drivers in the Extensions folder wasn't a viable workaround.  When I tried that, I think it lacked 2-D acceleration, which was instantly noticeable when scrolling was at a snail's pace.