Time Cave may be problematic, based on what their
FAQ says:
Q. How can I get messages to appear to come from my own address instead of from Time Cave?
A. All messages you send to any address other than your own will appear to come from your address...
This would likely cause some emails to be delivered to recipients' spam mailboxes, as the emails sent by Time Cave bearing your own email address would appear to be forged. This is because most email providers publish records that declare their email messages will originate only from certain IP addresses, servers, domains, etc.
If the origin of your emails doesn't match the records published by your email provider, then most spam filters will deliver them to spam, and some will outright block the email as undeliverable (Yahoo, for example, is very strict with outright blocking of some emails, with lots of false positives, legitimate nonspam gets blocked by them quite frequently).