Hello dogbone12,
It's perfectly possible, without rubbing of the tires, and if they rub with the edge of the rear fenders, you can literally (but carefully) pull the rear fenders with your own hands to gain a little clearance.
On the inside there's no rubbing either. In my older R4 cars, I even had 185/60 in the back, en they only needed a little hand pulling of the fenders, and both cars featured lowered suspensions.
The problem would be the front tires, BUT only in a lowered fashion like mine below, or if you'll go off-road and expect lots of suspension travel up front... Mine below are 175/70R13 (same width but slightly taller @ 70% of width) and they did in fact rub ONLY in the front and ONLY when turning and hitting a pothole at the same time, since the tire would travel a lot more and would hit the edge of the front fender, pulling it down. For this reason I switched those in the front to 165/70R13.
The wheels in the picture above are OEM, with the following dimensions: 13x4J (inches), 3x130mm PCD, -30mm Offset. The recommended
wheel tire by the manufacturer is the original 155/80R13, but it doesn't mean you can't get away with something wider. You'll also find below a description (in Spanish) from COFRE, the OEM manufacturer in Colombia, although sadly... they don't make them any longer.
