I see no reason why it wouldn't, but I'm not a doctor. Since the LES isn't actually stitched closed, but rather "snugged" inside the stomach wrap, it seems like what you're noticing is perhaps irritation and swelling in the LES causing a temporary reduction in diameter. Another source of pain may be tissues and blood vessels, etc., that were able to shrink/shorten as a result of the upper portion of the stomach being lifted and sutured around the esophagus. Logic tells me that once the stomach is released from its position, the weight of it (including food and water after meals) might pull on those tissues, perhaps causing pain.
Everyone's healing patterns are different, but this sounds like something you'll have to manage as best as you can while things return to normal. Stay in close contact with your doctor as well -- this is not a common procedure, and they should be giving you a lot of guidance. Internal organs don't heal nearly as quickly as scrapes, etc., on skin.
Keep us posted -- many of us empathize with what you're going through.