The easiest answer to this question is "almost never" -- but obviously there are some qualifications. So let me start with a real life story and then the qualifications.
A few cycle ago I got a call from someone who had taken the June LSAT and just received his score, in the upper 170s. He also had a strong LSAC computed GPA and was asking me if I thought he could get into Harvard next cycle (keeping in mind it was like roughly July 1 and Harvard clearly said on their website the application deadline was March 1).
I responded I had a hunch we could get him in "this current" cycle to which he referenced what I just did above and probably thought I was crazy. Again I'm not talking March, April, May or June -- we were submitting his application in July. So I made a deal with him -- we'd try now and if it didn't work I'd just stay with him for HLS and multiple other schools for the following year. Long story short -- he was indeed admitted (rather quickly) into HLS in late July.
If you can put your dean of admissions hat on for a second, schools will almost always make room (unless they are profoundly over committed -- but also keep in mind you lose deposited people all summer long who get of higher ranked wait lists) for a strong applicant. Have you ever had a boss in a professional career setting? For most reading this blog the answer is yes and thus you know making that person happy is pretty much the center of your professional galaxy. What makes your boss (the dean of the law school) happy? Raising medians! So if a school is looking to raise both, or even one, and they are fighting that fight against their competitors, of course they will look closely at a strong Feb. score. Most will look at a strong June score. The aforementioned "deadlines" are usually just there to try to get applicants to get their applications in. Data is king in admissions and early data helps you plan your entire cycle strategy. What they don't want you doing to sitting around with a complete application not submitting -- hence the deadlines.
My answer to the perennial question "is it too late" is always the following; just about every school admits people through August every year off the WL. So we already know there is going to be admitting going on and it isn't too late on that end. If you can jump in and help the school -- the vast, vast majority (not all) will let you apply well beyond their deadlines (I'd also note the data for this cycle might mean some schools are indeed going to be overcommitted earlier than they have been in the past recent years). The key is at this stage you do have to have at least one number that they need. You can apply early, say November with a some incredible softs and get admitted late cycle if you are below both medians. But a school probably won't let you apply in May with the same exact application. So to sum, have a number (or diversity ) they are looking for and you can probably apply a heck of a lot later than you know or you have been lead to believe. In admissions we see it happen exactly this way hundreds of times every year.
Edit update: I also failed to mention if you've applied to a school they will automatically get your Feb test score anyway. So even if someone is still telling you the really bad advice schools don't look at February LSAt scores -- they do!