I've dealt with this exact situation at home and it definitely works, but you need to be careful about a few things. Most modern luxury vinyl planks are rated for radiant heat now, but the key is checking that your specific product is rated for it - some brands cap out at lower temperatures than what radiant systems can reach, so don't assume all LVP is compatible.
The main risks are warping and off-gassing if the flooring gets too hot or if you're using lower-quality vinyl. Quality matters here: brands that explicitly market radiant-compatible products tend to have better dimensional stability and formulations that don't break down under sustained heat. You'll also want to make sure your radiant system has a thermostat that prevents the floor surface from exceeding what the manufacturer recommends (usually around 85°F), which prevents most problems.
One more thing - acclimate your planks to the room before installation, keep the radiant heat off for at least 48 hours after you install them so they can settle, and ramp the temperature up gradually afterward rather than cranking it to full heat right away. This gives the material time to adjust without stressing the planks.