If you think a corporate-controlled email address will provide you with a paper trail when it counts, you're delusional. It will, however, work against you whenever it's convenient for your employer.
That's one reason for every lawyer's advice on corporate emails: anything older than at most 2 months must get automatically deleted, even when there is no interaction from you, preferably without exceptions. Things that require longer term storage should simply be printed out and stored offsite. Anything you find offensive, anything about your employment conditions, ... should likewise be printed out and go to offsite storage.
This is not destruction of evidence because you're doing this as a standard policy "to save space and to declutter" (hah !), not as a reaction to being sued. As to why that argument convinces anyone when large companies can reasonably be expected to get sued very regularly ... But it is pretty well established in legal precedent.
You can download the emails of course, but then the accusation that, firstly, this is against your contract (it probably is forbidden in your contract), and secondly the emails could be faked will definitely be there. And of course, policies are likely in place to prevent you from doing this, even if they're very unlikely to be effective.