A true validation needs a real-world reference, not just another on-screen test image. Test charts can help spot obvious problems like crushed blacks or clipped whites, but they can’t confirm color accuracy by themselves because you’re still judging everything on the same display.

The most practical check is to compare your screen to a known external reference:

• Order a print from a reputable lab that supports ICC profiles, then compare the print to your monitor under good, consistent lighting.
• If you have access to a properly calibrated printer, printing your own image can serve the same purpose.
• Another rough check is comparing the same image on multiple displays calibrated with the same tool; they should look broadly similar, though monitor gamut differences will remain.
• A physical color reference card can also work, but that means buying something.

So yes, downloadable test images are worthwhile only as a basic sanity check for tonal separation and obvious display issues. For actual validation of color calibration, a print from a reliable lab is the best no-extra-gear option in your situation.