Can you Complete GTA San Andreas without Using Any Cheats?

The short answer is: yes. I've done it. It can be done.

However, not using cheats makes the game significantly more difficult especially at the beginning. I know people who claim that San Andreas can not be completed without cheats.

The main problems you face when you don't use cheats is that of money and weapons. You have probably got used to having the best weapons right at the very start without having to pay for them. Winning the gun battles at the start with an M4 is not very difficult.

As a result you will die more which is, of course, expensive. Some missions will require you to buy weapons. Having to retry these missions several times gets very expensive.

This is not to say that you can never use cheats. Cheats are fun. But you should not save your game after using these cheats. Go and save then play around with some cheats – turning off the console before saving.