No, there is apparently not any way to automatically mark e-mails read in Notes without an agent. But here's some more info that might help.
If your Notes admin won't grant you the rights to create private agents, then he doesn't understand Notes security and shouldn't be an admin. An agent that you write can only do what you already have the rights to do, so there's no reason to deny you the ability to create agents. (Furthermore, he can deny you the ability to create LotusScript or Java agents, if that will make him feel better, but still allow you to create simple agents and Notes Formula Language agents.)
If you can explain this nicely to the admin (without speaking as though you have the attitude that he's a moron) he might be reasonable and allow you to create an agent to mark your mail as read. Especially if you explain the purpose, and ask him to help you find some alternative way automatically mark certain mail read, if he resists. Since he won't be able to find an alternate solution, and this is such a basic requirement of any decent mail client, he will hopefully realize how silly it is to resist your request.
If you have rights on your computer to install software, and in the end he still won't allow you this right, tell him you're going to install Outlook (that'll bug him) but instead install something like Thunderbird, which can presumably mark mail read through mail rules. Thunderbird will have no problem making an IMAP connection to your Notes server. Perhaps he'll be so annoyed at the idea of someone using Outlook to connect to "his" Notes server (people who are unreasonable about granting access also usually seem to be very possessive about the company resources they're supposed to support) that he'll relent and give you the ability to create your agent.
As a very last resort, you could try getting him to create the agent with his rights, and ask him to make it run on your behalf. Read/Unread marks are per-user so I'm guessing it won't work if it runs normally under his rights. But if it runs under his rights, but on your behalf (this is a setting in the agent's security tab) I think it will work. Since I think the previous approaches are better, I've not tested this solution, and thus suggest it as a last resort.
Best of luck.