This is just my experience, so take it with a grain of salt:
I have several scripts that spoof my company's email server from my web server. I have found that as long as the FROM header and the RETURN-PATH header match the company domain, most spam-blockers will overlook the fact that it's a different IP address. In some rare cases you may need to ask the recipient to unblock your IP, but there is often a self-service link in the rejection notice so you don't even need to contact them.
It has also been my experience working with email admins that "whitelisting" is a very common activity. Just get your headers right so you don't end up on a major "blacklist" (i.e. - Barracuda's blacklist).
BTW - the RETURN-PATH header is the tricky one, and may require you to re-configure your sendmail options.