I've done it twice.

Some people ride a way down the I-10 frontage road which I briefly considered before choosing the 87>79 route through Coolidge, and I'm glad I made that choice. The way along the 10 is scattered riding over bad roads while looking at freeway traffic while the Pioneer highway route that I took was beautiful most of the way and at least has a little bit of elevation gain. It's about 6 hours if you're cooking.

The road from Chandler to Coolidge has a 5' shoulder that I would just refer to as a bike lane. It doesn't get much use so you can get some rocky or littered areas but nothing major, I didn't have a flat either time I did it, the first time I was solo, and the second time with a group a few of the heavier people got a flat. In Coolidge there is a gas station where you can refill your bottles, and you definitely should, because it's the last civilization you'll see until you get to Oracle Junction, which is basically Tucson, and is the longest stretch of road. There is no shoulder here, but the road is in good shape and despite the 65mph speed limit, the traffic count is low and mostly passenger vehicles. Both times I did this ride were planned to be at the lowest traffic periods, Sunday morning just after sunrise... actually started in the dark both times, so I may have been riding before most people are even awake.

Once you get to Oracle Juntion, there's a Mexican restaurant to refill bottles if you want and then a descent down into Tucson and it's mostly city riding from that point.

Here's a link to my most recent ride that way...
https://www.strava.com/activities/103359059