You will be breaching several license terms by doing that, not only Apple's but also YouTube's:
Excerpt from YouTube license terms, paragraph 5:
Your Use of Content on the Site In addition to the general restrictions
above, the following restrictions and
conditions apply specifically to your
use of content on the YouTube Website.
...
B: You may access User Submissions for
your information and personal use solely as intended through the
provided functionality of the YouTube
Website. You shall not copy or
download any User Submission unless
you see a “download” or similar link
displayed by YouTube on the YouTube
Website for that User Submission.
...
E: You agree to not engage in the use,
copying, or distribution of any of the
Content other than expressly permitted
herein, including any use, copying, or
distribution of User Submissions of
third parties obtained through the
Website for any commercial purposes.
There are probably other terms from YouTube that prevents you from distributing these movies though you own application. But just one of those caluses prevents you from distributin it though AppStore as detailed in Apple's terms:
5.1 You represent and warrant that: (a) You have the right to enter into
this Agreement, to reproduce and
distribute each of the Licensed
Applications, and to authorize Apple
to permit end-users to download and
use each of the Licensed Applications
through one or more App Stores; (b)
none of the Licensed Applications, or
Apple’s or end-users’ permitted uses
of those Licensed Applications,
violate or infringe any patent,
copyright, trademark, trade secret or
other intellectual property or
contractual rights of any other
person, firm, corporation or other
entity;
...
So the answer in short is no.