Well, assuming your ILR is a straightforward application, it should be approved on the day of the PEO appointment, and you will receive the BRP and your passport back within a week or so.
So,tThe only reason why you might not have your ILR by early-mid March is if, when you go to the PEO appointment, they determine your application is too complicated to be able to make a same-day decision and they send you away on the day and tell you to apply by post - in which case, you'll be looking at the average 4 months or so for processing by post. (Or if the application is refused, but this is rare).
So, unless you have reason to think your application is non-straightforward (i.e. you have criminal convictions or previous refused visas or entries to the UK) you'd probably be okay to book flights... however, 28th Feb is only 4 weeks away, so it might be a better idea to wait those extra few weeks until you have attended the appointment and you know for sure that your ILR has been granted - so you don't risk not being able to travel and having to cancel the flight.
