Not really. «Ку́рица» can be translated 'chicken' when it refers to meat, but when you're referring to a living chicken, chicken would be «цыплёнок».
Sorry, I didn't know 'chicken' can refer to adult birds too +_+. In Russian, we only have ку́рица for female adult birds, пету́х for male adult birds, and цыплёнок for young birds.
It’s a name of the dish, not a generic word for chicken.
If you go to a Japanese restaurant, you’ll find things like ‘Shake maki’ on the menu, but it doesn’t mean that ‘shake’ an acceptable way to say ‘salmon’ in English.
Similarly, if you go to McDonalds and find «Чи́кен МакНа́ггетс» on the menu, it doesn’t mean that «чикен» is an acceptable way to say ‘chicken’ in Russian.