There is a small percentage of users on my site that signup for the free trial using disposable email addressed like Mailinator, etc.
From a technical standpoint, if you want to ensure that it's a real email address, the typical way to do it is to send them an email with a link to follow back to you that confirms that they actually have access to the email address. That will stop you from getting completely fake or random email addresses, but there would still be no guarantee that it's one they check very often. (It may just be one they use specifically for things like this, and they only check it when signing up.)
This kind of approach is quite common, so you wouldn't be out of line or doing anything terribly beyond your user's expectations.
It does come at a cost though. You now create a two-step signup process instead of one. There will be people who will simply leave because it's too complicated, and there will be people who will leave because they don't actually trust you with their email address.
Consider how much value you provide to the users by having their real email address, and consider how many people you might lose as a result of taking this kind of approach. It sounds like it's only a small percentage, so it may not be worth your time to implement it, nor worth the hassle the users would have to go through. If most people had fake email addresses, it might be more worth it.
The reality is, if it's clear that you're providing enough value via the email channel, people will provide a real email address to begin with.
As far as negative consequences go, I think Eren Yasarkurt covered everything I could think of. Without a real email address, there's a good bet you don't have a way to get a hold of the user for important things regarding their account, like resetting their password.
Well the only way to prevent it would be to create an array containing those services names and checking at the register if the e-mail address contains any of the strings in the array. If the check returns true you could display an error message asking the user to use a genuine e-mail address.
Here are the negative consquences I can think of: