Most paramedic programs I know of (in the Pacific Northwest) require at least A&P1 or Human Biology prior to entrance. In Oregon I know we use to be required to take the entire A&P series I,II,III. However, There a few which integrate A&P within the medic course. Normally those are very "watered down" versions specific to EMS. No matter what, your gonna have to take some A&P to some extent to function as a medic.
Out of all the crap you learn many people would argue one of the most important aspects of it is A&P because its lays a basic foundation down for understanding. With out some basic understanding of it you will be a pretty crappy paramedic and will "left in the dark" on many calls. However, ignorance is bliss, plenty of stupid paramedics out there from "patch mills", and those who are dragging hose with handlebar mustaches, all practicing "meat head medicine." These guys don't think they need it because they have no clue whats really going on beyond following protocols as the word of god.
That is my 2 cents anyway
There are many, many paramedics out there who have never taken a formal (college-level) A&P course. Probably a big majority of them, in fact. It is still not required at any of the paramedic programs in my region, that I know of.
Many of those paramedics are really good at what they do. Can they name all the cranial nerves and their functions? No. Can they tell you all the bronchopulmonary segments of the lung, or even tell you how many times the bronchi divide? Probably not. But it doesn't mean they don't do a good job of providing prehospital care. The medicine is really a fairly small part of being a good medic, IMO.
If you really want to be "the best" medic you can be, then part of what I would do is study physiology/pathophysiology and pharmacology. There are lots of "______ for Dummies" type books out there that really have everything you need to learn the basics of this stuff. The important anatomy will come with studying the physiology.