The consensus is that overheating shouldn't be an issue if you eliminate the heater core, provided all your cooling system components are up to snuff. If they weren't you would have overheating issues with or without the heater core. If you decide to go with an electric fan, you may find that your current alternator may not be up to the task and may need to upgrade to a higher amperage unit. It may bring a quicker death to a marginal alternator. It is a good upgrade that won't hurt anything if you get the right kit, install it properly, and have a stout enough alternator.
My opinion: install a new heater core. While it isn't a "fun" job, it's a snap compared to modern vehicles, and you can get one from Rock Auto inexpensively. Sometimes in the Spring or Fall when using the defroster, you will appreciate having a little warmer air to keep the windshield clear. Not to mention, if you have a wife or GF, they tend to get cold even when we are sweating...
My $.02...