Absolutely! Members on Qeepsake Plus or Premium can text Qeepsake whenever something memorable happens.
You can find more details about texting Qeepsake spontaneous memories HERE.
Keep in mind that if you have a question that you haven't responded to in your text messages, your next text will be attached to that question.
If you want to send Qeepsake a memorable moment, but you haven't responded to the previous question, simply text "Skip" in response to the question you don't want to answer. This way, your memorable moment doesn't get attached as a question response.