If your SMP is worth its salt, you'll have access to a committee to write a composite letter for you either through the undergraduate school's pre-health office or amongst the medical school faculty teaching your courses. You should already be aware of this if it is being offered through your program.
I don't mean to judge your circumstances, but if you're trying to apply this upcoming cycle, you're setting yourself up to be extremely stressed. Asking for (and receiving letters) is a process that takes at least 4 or 5 months. 3 to take the class and establish rapport, 1 to ask the professor after they are likely to be through inputting grades and tying loose ends, and 1 to chase after them to submit it once they agree.
I wish it were easier and more straightforward, but recognize you are asking someone who may be up to their eyeballs with work to spend a half hour writing a letter they will not be paid for and that does not benefit them in any way. This is the time to mind your manners and brown-nose, because without letters, you can't apply at all... and if you are applying this cycle, you have very little room for error (IMO, you're already behind if so).
Remember that professors regularly dealing with SMP students have been to this rodeo before. It is a major emergency for you, but it's a major emergency for most of their students, and those alarm bells seem to blare semester after semester, year after year. It is unlikely that they will be maximally responsive the way you might expect given that, after a point, even professionals tire of writing letters to a faceless abyss and they may grow to feel that they don't "owe" anyone anything... and they would be right.
I say all of this in an effort to shake you by the shoulders so that you realize you have to prepare well ahead of time and create redundancies in your process because it can all go downhill fast if even one of your expected letters turn out not to pan out.
All of this to say, should you take the letter? Yes. Store it in Interfolio for a rainy day, if you can't get a better one. Thank them profusely. If you have a committee available to you, do everything you can to get into their good graces, because it doesn't seem like you're in a great position to get individual letters.