Yes, you can use a stock CPU cooler as long as your computer doesn’t run demanding tasks. If you mostly use the PC for general browsing, creating spreadsheets, or using text editors, a stock cooler is perfectly fine. A stock CPU cooler also provides adequate cooling for casual gaming.
However, if you want to run hard-core games and demanding apps, such as photo and video editors, you might have to replace the stock cooler with a more powerful air cooler or an AIO model.