you batteries and power wire are fine. increasing your alt output allows for larger consumptions of amperage. meaning you can run more amps or accessories with out having dimming lights bogging of the motor and other issues. 160a alt is pretty good for stock. remember that most stock alts are capable of running at 120% of there max output before thermally having issues. Whatyou need to figure out if what you max current draw can be with all of you accessories on. look up a current draw test on here or 12volt.com. that will tell you the actual health ofyou current electrial system. if you close to 70% of the max output with just the ac and stuff your good, with the set up you have you will not need another alt. onceyou find the current draw of the cars stuff you need to find the max current draw of the system you added as well as any added electrial anything and addit all togetehr. ifyou with in 120% you should be fine for a long time.
amps attempt to draw the same amount of current no matter what(depending on ohm load), if the amp actually gets the current matter on the health of your alt, batteries/caps, power wire guage and length, as well as a whole host of other variables. that being said most amps have a regulatesd power supply meaning that anywhere between 12.6 and 14.4 volts the out output of the amp is basically the same. back in the day this wasnt the case. but it is now.
honestly it cant hurt to increase the size of the alt, but only do it if you NEED to, or you plan on adding more amps. i would ALWAYS suggest the big three also.