Yes, depending on the format (HEVC can have a variety of compression levels, etc). If you are going from phone to AppleTV via Airplay, that's another variable.
The easy test is to link phone to iMac and import the video (cutting the airplay variable out of the test) and then try to play it on AppleTV from iMac.
The BEST test is to get yourself one or two LONG ethernet cable(s) you can run across the floor from iMac to router to AppleTV to establish a temporary but end to end ethernet connection. Then try playing problematic videos. If they play just fine over ethernet, you
KNOW it's the wifi and can work on ways to improve the wifi to make the wireless connection work. Sometimes this is as simple as changing the position of the router or AppleTV, even a few feet.
You can also hybrid it. For example, if you left the long ethernet test cable from iMac to router but then used wifi for router to AppleTV does it work fine? OR, if you went wifi from iMac to router but left the long test cable from router to AppleTV does it work fine? Either would narrow the probable wifi problem down to a particular stretch of space vs. involving all 3 parts.
If you find one of these ethernet tests fully resolves the problem, then you can start working on ways to resolve the wifi version of the same. If there is an essential ethernet connection from one link to the other and there's just no possible way to permanently make that with wifi, look into the ethernet over powerline options:
- plug an adapter like box into a socket near your router,
- plug a matching box into a socket near your iMac or near your AppleTV,
- plug ethernet cables into each box and your house power lines may be able to also give you a pretty good ethernet connection between each box.
Here's an example of one of MANY of that kind of thing...
Depending on how a home is wired, this doesn't always work, but it's easy enough to try and can thoroughly resolve an issue between a device and a router when wifi simply struggles.
Another possibility: if you live in an apartment and have freely shared your wifi password with friends & neighbors living close enough to you to access from their apartments (which can easily happen over periods of time- just one request in one visit for temporary access can lead to permanent taps of your wifi), they may be eating up some of your wifi pie, sometimes without knowing it. There's only so much wifi to go around. Even a few people biting into the wifi might be enough to cause wifi stutters when trying to watch streaming video on AppleTV. If this might be an issue, retest at a very odd hour when it is likely others are asleep OR change your wifi password to basically kick any "freeloaders" off and then retest.
Sometimes a change of wifi channel on the router will fix a problem in an apartment/condo/townhome environment with many competing wifi systems sharing the same space and channel. If you see a number of other wifi systems within your own system's reach in wifi preferences, up to all of them may be trying to use one channel. A different channel may solve your problem. I've visited friends in apartments and it can look like the airport when looking at the wifi list: 10-20 wifi systems within range.
And another: sometimes people gather videos they want to watch from the Internet (sometimes in a "yo ho ho... and a bottle or rum" type of way). These may not be formatted well for AppleTV and will not play at all or will stutter because AppleTV is trying to convert them into a format suitable for AppleTV on the fly. If this is the case, it doesn't matter about ethernet or wifi or potential wifi freeloading: you need a video that is definitely formatted for AppleTV. If you don't have anything purchased from the iTunes Store, purchase ANYTHING and DOWNLOAD it to your iMac (don't stream it from iTunes), drop it in the TV app or iTunes and then attempt to play it on AppleTV. If it plays just fine, videos sourced from other places may be at fault. If so, those need to be converted so that they are a format that AppleTV can handle well.
And lastly: I'm practically convinced that AppleTV and/or key AppleTV apps has some memory leak bug(s) and need a cold restart from time to time. I probably do this roughly monthly with mine... else, I will get some stutters in content I know is formatted for AppleTV. All this takes is unplugging, waiting a minute or two and plugging it back in. If you haven't done that in a long time, you might try that too. The cold restart flushes out all memory so that the whole pool is available for use again. After I do that, whatever was stuttering generally is not stuttering. I suspect many people never cold restart their AppleTVs and- if my guess about the leak is true- bump into some stuttering issues. Since its so easy to try this one, try it.