Sure....
Another bit of info: you CAN add insulation to the outside of a cheaper cooler.
But IF you are in a humid area, the cooler will 'sweat' between the cooler itself and the added insulation. This could cause a problem, depending on whether the water can escape and cause problems underneath with carpeting or a wood cabinet or floor.
Then you also have the added issue of the drain plug. Do you remove or peel back the insulation to drain, do you leave an opening, or try to scoop or siphon out water from the top...not easy to do.
And, draining the cooler daily will tend to dribble some water back into the insulation you have added. And it WILL find its way to your carpet or floor.
Some coolers have a 'garden hose' attachment for draining....this is handy if you can make use of it.
I keep my heavy-duty cooler near the door or tailgate, where I can swing it out and drain the daily melt into a small bucket, where I use that cool water to chill a few canned drinks or juices. Then later in the day when its warmed up, that water can be poured into a sprayer and left sitting in the sun, for daily clean-up duties, showers, hand-washing, etc.
Just don't reuse the melt-water for drinking or cooking.