NO.
The components you see on the battery are BASIC thermal and over/under voltage cutoff components more than likely, they're not meant to control a charge they're meant to keep people such as yourself from catching the house on fire =) If the circuitry acts as you describe in theory you could rely on a 5V 500ma rail to charge the cell safely, but again that circuitry is meant as a failsafe not as a primary charge controller, it's your house that'll burn down if you're wrong.
I'm not sure why you even asked the second question, how do you intend to charge a 7.4V battery (even at the low cutoff of 6.4V) with a 5 volt source?
Simply speaking if you don't know EXACTLY what you're doing then YES you absolutely get a proper charger.