I think 1000w would still put too much of a strain on that alternator, and yes that will cause voltage drops that WILL hurt your amp. In your case there is no way around a HO alt (unless you like spending way more money than needed).
I'd hook it up and monitor your voltage. It's not like the amp will draw 100A continuously - not even close. If you're sagging to 12 or lower you'll know you need to reduce the gain and go easy on the volume until you can get your HO alt. If you maintain at least 12, and get around 13 most of the time you should be fine.
Your car's voltage fluctuates a lot, and there's a lot of gray area around when is the right time to go with a HO alt. You're always better safe than sorry, but at the same time, why spend the money if there's really no reason to.
A healthy battery should rest at around 12.5v, for it to charge you need to see 13v+ most (90%?) of the time.
I used to run 1100w with a 75A alt. At idle I'd see around 12-12.4v, but at any RPM above 1.5k or so I had 13.6-13.8v. Obviously it's not ideal to run like that (with the sags to ~12), but as long as your alt will charge the battery you won't end up stranded on the side of the road. However - having that much stress on the alt will most likely shorten its life. The 75A alt I had died after 2 years in that state - then again, it had 226k on it.
I think i will hook it up and get a voltmeter so i can watch it while im driving, and just listen to it around 500-750 watts, and just crank it up to 1000-1200 for short periods. Should i be alright? Would that extra deep cycle battery help me out if i wanted to run it with not a whole lot of power, then push it up everyonce and a while for those short bursts?