The answer is No and Yes Both . No,because of Firefox product updates are come from Mozilla.org while Internet explorer which is a Microsoft Product and both are using there own preferences and settings. So, it having no such effect on firefox if you are updating IE updates . Yes, because with each updates Microsoft provides some patches to IE which improves his own stability.

Note that IE is part of the Windows OS, it is deeply integrated, and other Windows components use it to connect to internet. IE security updates are needed to address security vulnerabilities in the Windows OS and it also updates other software components (system DLLs) at times.