Absolutely! Members on Qeepsake Plus or Premium can text Qeepsake any time 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, your next text will be attached to that question. More about how texting works when you have multiple children/journals
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.