Yes, you can seal an old concrete floor as long as you remove stains and repair damage before sealing. Remove everything from the garage and clear the floor throughout with a concrete cleaner and power washing. Fill in cracks larger than 1/8 of an inch wide and remove all grease and rust stains before sealing. Make sure your concrete is fully dried before applying sealer.

Concrete is extremely porous. Without a proper sealing, it will absorb just about anything it comes in contact with, including water and ice. During the colder months with freeze-thaw cycles, this could cause the concrete to crack and become damaged in other ways. You always want to seal your cleaned concrete surfaces after they’ve completely dried out.

Polished concrete floors also have downsides. Some homeowners, for example, might dislike the coldness of the material (though area rugs can help warm up the space). Concrete floors are also hard, which isn’t always ideal for children and pets. What’s more, these floors are susceptible to cracking, and repairs can be costly. Some homeowners might not like that installation isn’t DIY-friendly. 

The prevention steps are essentially the same, no matter the patio material. Keep the surface clean and maintained. Ensure there's no debris buildup, and cover the whole thing in a quality sealant. If it's the start of a season or it's been a while since you've cleaned the area, use a pressure washer.