If the Anno games represent a simulation of the respective time period, do I get to play as a Pirate in Anno 1701?

No you do not get to play as a pirate. The pirates are a faction that you encounter ingame that may or may not have a base on some small island. You can trade with them, bribe them to attack other factions (iirc) or destroy them.

Check out Sid Meier's Pirates! if you're looking for a stellar game about being a pirate.

Oh I'm a huge fan of SMP.

So what is Anno then? Is it like Sid Meier's Civ? Is it different? How so? Whats the aim of the game?

Also, how would you rank all the Anno games?

Ah, I see. So kinda like a fusion of Sid Meier's and Stardew Valley? You can set up what you want and do what you want like SDV, but in the pursuit of expansion like the Civ games.

Yeah, I hate uPlay too hence planning on buying all the Anno games in GOG whenever a sale comes up. I have Anno 1602 on uPlay but its so buggy its depressing. GOG does a good job in optimzing older games.

So what are the core differences between each of the Anno games? Clearly, its set in different eras, but doesnt the core stratgy remain the same?

I couldn't really say what it's a fusion of tbh. The closest I know of is the classic sierra city builder series Caesar 3, Pharaoh etc, except without the random walker system. But like you said you do pretty much set up the industries to expand. Or upgrade rather. Your citizens have levels (pioneers -> settlers -> citizens -> merchants -> aristocrats) and you want to get them to the highest level to get more money so that you expand your fleet and military forces. But to do that you have to supply more and more exotic goods.

I haven't played all of the anno games (only 1602, 1503, 1701 and 2070). But yes, the core strategy is pretty much the same between all of them: In 1602, 1503 and 1701 it's always a rush to make your first ship and reach citizen levels, the level at which you stop having to worry about going bankrupt.
From 1602 to 1503 the main difference is a more complicated resource system, food/goods distributions via placed stalls and aristocrat houses being built rather than upgraded. From these points of view 1701 is a lot more like 1602, except with some extra bells and whistles here and there.
1404 from what I've seen appears to be an across-the-board improvement on 1701.
2070 is a bit different in that you can choose between two different branching tech trees : more industrial / or more green. Each with advantages and disadvantages.

Personally, if I had to recommend an anno game to someone then it would be 1503. At least before moving onto the 3D ones, in which case I would jump directly to 1404.