What will be the time to charge a capacitor if there is no resistance?
In a perfect world, the capacitor would charge instantly. This is clear from your equation: the charge time is
$$
t \approx 5RC
$$
so if \$R = 0\$, then \$t = 0\$.

However, batteries are not perfect voltage sources. They have an effective resistance, which is on the order of 1 ohm, so the time to charge your capacitor without a resistor is approximately
$$
t_{real} \approx 5C
$$
This resistance depends on what type of battery, how dead the battery is, etc... so this is only a rough estimate.