So, lets say there's about $1.8*10^{21}$kg of water on the surface of the earth (this excludes hydrates and stuff in the mantle, but the surface stuff seems like the bit most likely to be deposited by impacts after earth's formation).
Given the density of ice, $920kg/m^3$, that much water would form a solid sphere about 776km in radius. That's Quite Big, by the way... the Chixulub impactor that kicked off the Cretaceous-Paleogene extinction event wasn't likely to have been bigger than 81km across. It is bigger than every asteroid (Ceres has a radius under 500km) and as big as some of the larger moons in the solar system... Iapetus is a similar size and mass and is also largely made of ice so it is a good representative for your impactor.
Here's a size comparison of Earth, the Moon and Iapetus, so you can get a handle on what you're asking about.

(By way of a bonus, the massive crater Engelier is just about visible on Iapetus, and makes it look a bit like the death star. It is a mere 500km across, far smaller that anything we'll discuss here.)
It is at least smaller than the Theia impactor believed to have created our moon, which was believed to have been about 6000km across. There are theories suggesting that much of the Earth's water did arrive during the Theia impact. I won't go into the Theia impact here, but instead consider only a single delivery of ice, probably after the moon was formed and the Hadean era ended (otherwise subsequent bombardments might have blown the water away into space).
Lets assume it is hitting crystalline rock, there being no water or sedimentary minerals on a waterless world. You can now throw these handy figures and assumptions into the Earth Impact Effects Program. I picked a conservative impact velocity of 11km/s (it is a bit unlikely for it to be lower than this, and at this speed it is more likely that some of the delivered water will stay) and a 45 degree impact angle (other angles don't make much difference, which isn't entirely surprising). Summary for those of you too lazy to follow the link and fill in the form for yourself:
- Initial crater 606km deep, 1710km across. Given that Earth's crust is no more than 90km deep, that means the mantle is very definitely exposed. The hole will fill in with ejecta, of which there is quite a lot... it'll end up about 3-4km deep.
- Final crater diameter: 4540km, once the surrounding land has finished falling into the initial hole. This is vastly bigger than the biggest hypothesised impact structures ever found, MAPCIS.
- Despite the impact energy being measured in exatonnes, the calculator doesn't suggest that you'll get a really interesting superheated fireball as the impactor vapourises. I'm slightly dubious on this, but as I'm not an expert on banging rocks together and the authors of the application are, I'll defer to them. Certainly, the behaviour of objects undergoing a hypervelocity collision is unintuitive. This increases the chance that some of the water will actually survive the impact and stay put.
- Debris from the impact (like, lumps of the stuff, not just dust) will fall over 5000km from ground zero.
- If it hits at the right sort of place (say, at the equator) it could change the day length of the earth by a bit... for a 45 degree impact, the change is of the order of ±15 minutes.
The sedate impact velocity is required to minimise the chances of massive post-impact heating. Hopefully the impact pressures are low enough (relatively speaking) and the energy release spread out over a long enough period of time that what you get is a huge explosion of rock and steam that boils and buries an area larger than North America, rather than a multi-thousand-degree fireball that propels debris out of earth's orbit and generates large quantities of light gases that can escape the atmosphere. If the latter occurred, you'd need to deliver even more water, and then the impact energies would be even higher and more volatiles would be lost... and so on. You can see why many smaller impacts are preferred. Some vapourisation will inevitably occur, but it calculating how much is definitely out of my league.
The aftermath of the impact will involve a lot of dust lofted into the atmosphere which will also be filled with a great deal of steam. There was significant global cooling after the Chicxulub impact, but that didn't involve pouring a bajillion litres of water into the mantle, so whether the energy stored in all that steam will dissipate and rain out before the dust settles, or whether you'll end up withno significant coolings and a thick, hot water vapour atmosphere for a considerable time afterwards I don't know... again, that sort of guesswork is out of my league.