Nope, tubes tend to deflate immediately and without warning. Think about the typical scenario of picking up a nail or screw in your tire. As soon as that pointy object gets pushed through your tire it will cut, slice the tube as it keeps getting moved around or through the tire every rotation. On a tubeless tire, sure you'll have a puncture but the tire rubber itself will sort of self heal around the object so that you end up with a slow leak that most times you won't even notice until much later or once your pressure gets low enough you'll feel the bike's steering get sluggish or start to wander etc.
Bottom line, tubeless tires are safer but knocking on wood here, the only bike tires I've ever had go flat were on my dirt bikes. And besides if your bike happens to have spokes, then you don't really have any option except to run tubes anyway. Sure you can get the rims sealed but it isn't always foolproof. Both my wife and I have been riding bikes with spokes and tubes for over 6 years now with no flats.
Check your pressures regularly, at least weekly if not before every ride and inspect your tires the same. I'm in the habit of glancing at my tires every time I get on the bike and at least weekly the bike gets put on the center stand and the tires inspected properly looking for punctures, bubbles, wear etc. Only takes a few minutes and we only have two small contact patches keeping us on the road so I like to make sure they're in good shape.
