No-one can tell you whether you will be able to eat the meat - it's a very individual and highly personal thing. And it's not rational, it's of the heart. Don't knock it, it means you're human.

What you have to decide right now is whether you want to be able to have any other livestock in due course. If yes, then you have to 'man up' and make that journey now - or you can only have as much livestock as you can cater for as pets, just as you can only have as many dogs as you can cater for at one time.
When I took Gaby in, I knew damn fine I wouldn't be able to eat her meat if I got it back that day. But you don't. By the time it's been slaughtered, cooled and butchered (assuming from your post you are having it butchered for you), more than a week has passed. And you don't have to eat any of it straight away if you don't want to - give some away or sell it fresh, freeze the rest, eat some when you're ready. If you are never ready, give the rest away, or sell it, or swap it for pork from someone else's pig.
In my case, by the time it came back from the butcher, I was ok to eat it. BH was a little uncertain about it the first couple of times we ate meat from the first pig, but now he loves it. I have to say, he doesn't get as attached to them as individuals as much as he did that first pair, though.
I am now okay about it; I don't like taking them in, and am very sad for a day or two when they go, but I love filling the freezer, and the arms of relatives and friends, with beautiful succulent home-reared pork. And I love love love serving up the best roast pork anyone can get anywhere to family and friends.
I also love getting the next pair, or breeding a litter at home, and having all the fun of rearing weaners again.
So in my case, and BH's, I would say that yes, it does get easier. It still affects us but the benefits are worth it - to us.
But if you decide now, or after taking this first pair in, it isn't for you - don't beat yourself up about it. And certainly don't make yourself miserable or ill over it.