Yes. Copper-based treatments (many ich medications are copper-based) can set plants back and even kill some (copper is a heavy metal and thus highly toxic in elevated levels, though a nutrient in a very small amount), depending upon the plant species and the product. Salt (another common remedy for ich) can also affect plants, some more than others.
In planted tanks I have used a combination of raising the temperature to 86F and using CopperSafe which for me has been less of a problem (it is not as strong as some products), though some plants were affected. The increase in temp may be a factor too of course.
One option is to put all the fish in a separate quarantine tank and treat them there. With cardinals, higher temps are fine so you could really turn up the heat. This quickens the ich cycle, and some suggest it may kill it if around 90F, so I'll mention that for what it is worth. Leaving the planted tank empty of all fish for 3-4 weeks will kill off any ich in that tank, as it cannot survive without host fish. I don't know what fish or how many you have, so this may be more work. Treating the main tank is possible, but I will let others detail methods other than what I've suggested.
Byron.