Yes and no.
Item price doesn't include 'externalized costs' E.g. An item produced in China or under Trump's toothless EPA will likely have greater associated pollution compared to a similar product produced in a nation that has strict pollution laws. This one is hard to find information about. All the 'externalized costs' estimates I've seen are just that: Estimates. Ranging in quality from some careful methodology to wild as guesses (WAGs)
Item price will include stuff that has no relation to sustainability:
Snob appeal. While a Rolex is a fine watch (if you like mechanical watches) it isn't 100 times less sustainable than a cheap third world country knock off.
Marketing. Companies spend enormous amounts of money to try to convince you that their product is somehow better. In some cases this is true, but the marketing only contributes a small amount to the environmental cost.
Retail markup. Women's clothing is often marked up several hundred percent. Men's clothing less so.
Relative worker wages. The exact same product produced in Thailand will be cheaper than the same item produced in Germany.
So let's modify out measure:
Look at the wholesale cost of a similar commodity item.
This avoids most of the marketing costs, the snob appeal, and a good chunk of the wages issue, since most commodity items are produced off shore.
This is still only an approximation, but it's a useful one to use.
For some items a commodity product doesn't really exist: Professional grade digital cameras come to mind. In other cases, there is a huge variation of quality in the commodity item. I've encountered this in Brussel sprouts and desktop PC's
Digging deeper requires knowing a lot of specific information about the manufacturing methods, the place of manufacture, and will require decision making about the relative environmental impact of using steel vs plastic vs fiberglass; using electricity from wind, hydroelectric, coal or nuclear.
The method can be generalized a bit by dividing it by the weight of the item. So, for example, figure out the price per pound for cars. Once you get away from the brand appeal factors, the cost per pound is surprisingly uniform. Compare the price of baseline equipped pickups to semi tractors, and you get similar numbers.
Another valid ratio is the cost/year cost/mile. A Widget that creates twice the pollution, but lasts 5 times as long may be worth it. E.g. Nylon climbing rope versus manila rope. Kevlar canoe vs wood and canvas canoe.
I received the following comment:
No. Quite often the more sustainable option is more expensive (organic veg vs. conventially farmed; beef from cows raised on deep-ley pasture vs. soya-fed; electric car vs. petrol car; gas boiler vs air-source heat pump; taking public transport vs. driving). – aucuparia
Accuparia has a valid point, and gives another factor to my 'yes and no' answer.
However, dig into the examples:
Organic veg are more expensive mostly because they are a fad. The increased cost is either due to marketing, or is a temporary aberration in the market as supply catches up with demand, and is in part due to the difficulties getting certified as organic. Additionally, organic growers aren't working at the same scale, and don't have the economies of scale. We're starting to see large organic operations. Their prices are very little different. Reports I've read about farmers who have gone organic indicate that production cost is initially higher, but once the soil has been rebuilt, the net result is a lower yield per acre that is more than compensated for by lower input costs.
Pasture raised beef is cheaper than feedlot beef once you take into account the externalized costs of the feedlot's manure problems. Again this is market perception.
Until recently the higher cost of EV's presented a quandary. In my reading there was serious doubt whether the TCO of an EV was actually less than an ICE, due to the upstream costs of the battery. Now it's quite clear that the EV is lower cost than an ICE.
Public transit is usually cheaper than driving, especially when you factor in fixed costs and depreciation.
