Stun mechanics are very hard to balance and are generally a bad idea. Ideally, they should be implemented in a way that gives both the attacker and defender meaningful gameplay, but this is exceptionally hard to do. Most of the stun mechanics I have seen boil down to "hit the player with X to turn their game into a screensaver", while the counter-play options are usually just as shallow or non-existent. The worst examples of stun I have seen typically involve permastun, which has absolutely NO counter once it starts and will result in the defending player watching helplessly as they die (for however long that takes). These ARE NOT good stun mechanics, they are too shallow and do not offer meaningful gameplay for either side of the engagement. The attacking player gets a hollow victory due to the easy kills that require little to no skill, and the defending player feels helpless as they did not get ample opportunity to defend themself.
The only group of players that I can see benefiting from a stun mechanic in any game would be gankers (who will stun people to make fights even more one-sided) and griefers (who will stun people without killing them). I personally do not see ED as a game that encourages these kinds of behaviours. Yes it allows for these behaviours to exist, but it does not encourage them. Adding something like this would dramatically shift the PvP environment of ED towards these kinds of behaviours, which is something that I do not believe the majority of the playerbase is either prepared or willing to see (see any of the number of threads ranting about ganking and griefing).
As for OP's suggestion itself, I'm going to have to say no. Fankly, the EMP module would offer FAR too many advantages with virtually no disadvantages. Let's compare the EMP module to the grom bomb as an example. The grom bomb is an unguided missile that forces the target's FSD to reboot (up to 10 seconds depending on engineering), requires the attacking player to give up some of their firepower, requires skill to use (only available in fixed-forward firing with a low shot speed), and can be hard-countered by out running or dodging the missiles, point defence turrets, and ECMs while also being soft-countered by the fast-boot FSD modification. By contrast, the EMP module would completely shut down the target player's ship (probably for around 20 seconds like the thargoid version), does not require the attacking player to sacrifice firepower, does not requires skill to use, and can only be hard-countered by either getting far enough away from the attacking ship (which isn't always possible) or by winning a very short high-skill timing minigame. If I could use an EMP module on my ship instead of a grom bomb, there is absolutely NO reason why I wouldn't. The EMP module has a more debilitating effect on a longer timer, requires far less skill to use, does not require me to sacrifice a hardpoint, and is MUCH harder for the defending player to avoid. Simply put, the EMP module would be OP to the point of being broken.