No, it will not. Without re-hashing too much, the Debian case was different, in that the changes involved incorporating software patches (code) that had not been reviewed and accepted into the Mozilla code base, and the maintainers wanted to be able to include those patches at their discretion, independent of Mozilla's review and approval process. The Ubuntu change is a configuration change, where the default Yahoo! open search plugin and the default search order will be changed, but the application executable will not. Canonical/Ubuntu, as stated in the comment above, does have a distribution agreement in place with Mozilla. Part of that agreement is that any changes to code and/or config that differs from the default will be reviewed by Mozilla, and will not be included in a Firefox-branded product without Mozilla's permission (http://www.mozilla.org/foundation/trademarks/policy.html). Canonical believes this change is in the best interests of sustaining the Ubuntu project, and Mozilla has given permission for that change to be made.
If you do come across distributions of Firefox that exhibit the type of behaviour you outline,we'd like to hear about it.