Not really? All the story elements of Shadow of War are wrapped up at the end of Act III- there is an extremely minor epilogue at the end of IV, in cutscene form, but it's thin soup indeed for the hours & hours of punishing, storyless sieges it takes to get there.
Overall, it's best to think of Act IV as siege-mode expansion pack. Play it if you want to get deep into the nitty-gritty of sieges, and see all the various orcs the game can conjure up. It's also the best way to get XP and loot, if you're looking to perfect your Talion, or unlock the high-end skills & Legendary Items. And lastly, defeating Act IV is the only way to get all possible achievements. If none of those things particularly appeal, you can walk away at the end of Act III having missed nothing. And of course that epilogue is on youtube, if you absolutely must know.