Can a webpage appear in iOS Safari without any Safari UI even if someone visits the URL in the browser?
When you launch a web app by entering the URL in Safari it runs in the Safari app. But when you launch a web app from the springboard (home screen), it runs in different Safari app. Hence the lack of Safari UI in the that case. What you want isn't possible. And it's actually a good thing because the Safari UI offers option you might need to use ('mail link to this page', 'Tweet', 'Print', ...).

What you want to do may be possible through some kind of hack if you jailbreak, although I doubt it.