I've incorrectly filled out the "Have you ever been refused a visa" section of the UK visa application. Is this likely to cause a rejection?

No.

This is assuming that you reapplied for a T4, after having had the refusal for missing documentation, and therefore were granted a Tier 4 visa (or you would not now have only the one refusal). This establishes that the documentation issue was relatively minor, hence of limited relevance to your current application.

Having already messed up once (missing documentation) to do so again (sign off as complete and correct when not) is abominable but for the applicant to be a bit of an idiot is not reason enough to refuse a visa.

You may have had a better chance had you abandoned your incorrect application (eg never booked the appointment associated with it) and instead started afresh but I doubt any difference is significant.

You have attempted to rectify your error, both by amending the printed version of the form and by e-mailing the Home Office (I hope you take a copy of that e-mail with you to your appointment). So it is evident you were not attempting deceit (or at least had second thoughts about it!).

Also, you are lucky that the prior refusal was from the same country as you are now applying to, making the follow-up responses (country, visa type and date) less critical. Because the refusal was by UK and that is where you are applying there should be an accessible record, and the follow-up responses were probably only to help investigation where rejection was by a different country.

You do not provide details of your current application (nationality, where you are applying from, visa type, duration, personal status, documents submitted etc) and it seems quite likely that even without the incorrect filling out you were never going to be granted a visa but the incorrect completion is not likely to cause rejection of itself, though does add to the risk.