Submachine guns eat ammo very quickly. You'll maybe survive one fight or two, depending on your proficiency - and then you're that barbarian with the death stick whose death stick isn't working anymore, but has made a people who are famous for holding deep grudges for years and coming up with very creative punishments for their defeated foes extremely angry.
Also, it's not like Romans don't have ranged weapons. They were experts at using the sling, which can kill you at the same distance as a firearm. They had bows and crossbows, throwing spears, etc. You are not prepared for any of this.
You're not really thinking this through. You started from the premise that this will fail and are only presenting thoughts that support that premise.
The gun gets you whatever you want, including armor and whatever else. Kill one person, hopefully Caesar, and do it in front of as many people as possible. Then your demands start and must be met ASAP.
There are plenty of possible paths to success just as there are to failure and neither is guaranteed.
Not that easy. Sure you could kill ceaser, but you can't kill everyone who might take offense. you can be killed in you sleep. you can be killed by a mob as eventually someone gets through.