I currently use a hosting package that is used both for the website and emails. Since it is a shared hosting the IP is sometimes blacklisted so our emails are considered SPAM and are bounced back. I want to setup Google Apps account, only for the email addresses, to avoid the situation of emails considered SPAM because of blacklisted IP. I plan to setup the DNS (provided by the domain registrar) with a domain mx records that points to google mail servers, and keep the A records (for the website) to point to the shared hosting server.
I wonder how will the destination email server react in a case when we send email via google mail servers, but still use our own domain name? Will the destination mail server still check whether our shared hosting IP (resolved with our domain name) is blacklisted, or it will only consider the google mail server IP?