Hello. Could I still apply for visa free stay, if I have valid Chinese visa in the passport?

Yes, you can. Anyway, you have to travel on eligible itinerary through China described by formula:

A - B - C countries where China is a country B

You should just take care that you declare in the country A that you will travel to the country C through China (country B) using 24 or 144 hour visa free transit. Also, you should be very focused upon your arrival in China and explain immediately your intentions because if you don't do that, it could happen that an immigration collect your remaining entry.