Yes. If Outlook Express (OE) had trouble sending the message it would remain in the Outbox.
(Checking a web based Sent Items folder will not always work, as each e-mail program has its own Sent Items folder. OE sent messages will be in the OE Sent Items folder, while webmail sent messages would be in the webmail sent items folder.)
In the future if you want to be certain that a message is delivered, you can turn on read confirmation. This can be done on a message by message basis or for all messages.
To activate for an individual message, go to the Tools menu, then Request Read Receipt, prior to sending.
To activate for all messages, from the main Outlook window, go to Tools->Options, then select the Receipts tab. Check "Request a read receipt for all messages".