That would be a checked bag as even 62" is well beyond the permitted size for a carry-on.
To answer your question, the airlines will included wheels and handles in their measurements so it seems like your bag is technically too large. While it is possible--maybe even likely--that a 64" bag would not be challenged as long as it isn't over 50 pounds (but as the PP notes, it's not hard to get a bag that size over the weight limit), if it does get measured your looking at a $75 oversize bag charge. At that point--unlike an overweight bag where you could shift something to another checked bag--you're pretty much on the hook for the charge.
So to be safe, I would go with another bag and not risk it. If you're willing to gamble on the $75 for one or both ways, then have at it!