I'm new to classic car ownership. Just obtained a '61 LeSabre with 364 V8, heater core leaking. Can I run a hose from inlet tube to outlet tube on Waterpump to avoid coolant running to Core? Will this create any further issues?

It depends on where you live. If you live in cold country, it will present a big problem in January..!
It's not a problem at all, it's done all of the time. Most vehicles use two different size hoses, 5/8 and 3/4, so go to the nearest auto parts store and buy an adaptor designed for just this situation, or make one yourself. Then you have six months to change the core before it snows again..!

Thanks for the advice...luckily, this car doesn't move in the winter...