Personally, I think that you should, in that accent marks are helpful. But:
(a) Plato wouldn't have known what an accent was, anyway, the whole thing being a conspiracy by later schoolmasters
This is true—but the "conspiracy" was just to write down the way things were already being pronounced. The accent marks were meant to be descriptive rather than prescriptive.
(b) the sooner I get to grips with Homer and Plato directly, without a lot of Hellenistic pedantry
Homer similarly wouldn't have known what an "alpha" or an "epsilon" was: all of his poetry was spoken aloud, not written down until centuries later, but it's a lot easier to follow his work nowadays if we use the alphabet. Socrates similarly was a major opponent of writing and didn't approve of Plato taking notes on everything.
In the end, the accent marks help make your pronunciation more accurate—but most likely you aren't going to be conversing with many ancient Athenians. So most classicists aren't too worried about a historically-accurate pronunciation.
Instead, I see it as equivalent to pronouncing the difference between omicron and omega. Lots of people don't, including the vast majority of modern residents of Greece.
But if you make the omicron/omega difference part of your mental model of Greek, it'll be easier to remember which one is used in a particular word, and it'll help you can write out accurate Greek as well as read it, without having to check a dictionary for each word. Suppose you've learned the word moros, for instance, without distinguishing omicron from omega—every time you see it, or want to write it down, you'll have to check a dictionary to determine if it means "fate" (second letter is omicron) or "idiot" (second letter is omega).
Accents are similarly just something that has to be memorized along with each word (*), but the same holds true in English: it's how we know to say giráffe but pánda in loanwords, just pure memorization. I personally find the tradeoff worth it; your mileage may vary.
Most importantly, though, pick a system that works for you, and just stay consistent with it! Sticking to a single pronunciation system, whatever it is, will help your memorization more than switching horses mid-stream. Erasmian pronunciation, Modern pronunciation, Reconstructed pronunciation are all viable and all have their adherents; as long as it works for you, and helps you read the language, that's what's most important.
(*) In fact, in some words (notably finite verbs) it's totally predictable and doesn't have to be memorized! So I'm overstating the difficulty a little bit.