Pretty much - the change chance is on each visit to the square where someone digs, so the general crappiness of the UO RNG can sometimes work in your favor, and sometimes not. (sometimes a place stays the same color for dozens of visits, sometimes you fail 6 times in a row on what should be a 95% smelt chance, turning 64 ore into 1 ingot). Sometimes you can get an area stay the same for weeks - sometimes you can have something change after one visit. I'm to the point that I'll typically just go mine an area I know has lots of colored ore in high percentages, and use both the Prospector's tool and Gargoyle Picks, and come back an hour or two later with 100 or more ingots of every color from Shadow to Valorite.
And, if you need gold or agapite, it's easier to farm Blackthorn's basement for gold ore from the Golden elementals (take a combat miner down there, and smelt as you go - you can use one of the gold smelting talismans' 3000 charges in about an hour), then after you get a few thousand gold, get one of the gold-to-agapite cauldrons and convert 3000 gold ingots to 1000 agapite. The BODs that produce the talisman and cauldron are pretty cheap to fill.
Trees change similarly (but a change for the ore doesn't effect the trees, or vice versa), but since trees for higher woods are extremely rare by comparison, it's much worse for the lumberjack.
There are a few trees in Eodon that approach the old "magic trees" in terms of output (they eventually run out, but after hundreds of chops, and usually quickly refill, sometimes before it runs out). While I was training a lumberjack, I had one go from Oak, to Ash, then back to Oak, over the course of about 6000 logs. I'd been constantly chopping the entire time. So, the tree had changed type during a reset/refill as I chopped, then did it again later. The same tree/resource square had stayed the same over about 2000-3000 chops (tens of thousands of logs) over the previous couple of days.