Would it be safe and not cause further damage to the car if I were to drive it 1/4 mile on a dirt and somewhat bumpy road? (The towing company under my policy won't go on dirt roads.) I've been told that the issues is that the shock is broken.
Not only is the shock broken but the upper suspension control arm has collapsed too. Driving the vehicle would likely cause further damage to the tyre, CV unit & possibly front differential/bearings too as there is a lot of force being transferred through that drive shaft into the front diff with the upper control arm collapsed.
Unless you have some sort of trolly to place the front right of the vehicle on to, your only other option other than a front end lift is to put a lot of weight onto the rear left of the vehicle to help unload the right front wheel. Then perhaps an attempt at moving forward might be possible, but do it very slowly.
Is it safe? Safe is relative, but you won't be going far in that car anyway - it's broken as broken can be.
I assume you're getting the car towed to a garage for repairs. I'd suggest getting a pair of front shock absorbers online, and then paying for a mobile mechanic to come out and install them for you. That should get it moving again, and the mechanic will be able to tell you what else is broken. After those repairs, you will be safe to drive it to a garage for an alignment.