Does this sentence make sense grammatically?

If not, I would like to sit down with her before the meeting to quickly acclimate myself with how things are presently being done.

You "acclimate to" not "acclimate with." The sentence is wordy, but, with the change, it's correct.

Several comments:

1. The word "myself" is misused here (as it almost always is) - you should use "me" in place of "myself." The only time you should use "myself" is when you are acting upon yourself - as in "I gave myself a bath." But when other people are doing the acting, the proper word is "me." So here it should be "to acclimate me with ..." or better yet, rewrite to avoid this problem entireley: "so I can become acclimated with.."

2. You are misusing the word "presently," which actually means "soon" or "in the near future" - it does not mean "in the present." You should use the word "currently."

3. Some people would say that you should avoid the split infinitives - where you currently have "to quickly acclimate myself " should be "to acclimate myself quickly," and "things are presently being done" should be "things are done currently," but personally I think that's nit picking.

4. You have the phrase "become acclimated with" when what you really mean is "to learn about." I am a fan of keeping writing simple and clear.

Put all this together, and I think this sentence is better written as:

"If not, before the meeting I would like to sit down with her so I can learn how things are done currently."

You wrote:

If not, I would like to sit down with her before the meeting to quickly acclimate myself with how things are presently being done.

Try This:

If not, I would like to sit down with her before the meeting to get acclimated to how things are being done.

1. The word "myself" is misused here
His use of "myself" is correct.

"If not, before the meeting I would like to sit down with her so I can learn how things are done currently."
"Currently" should be changed to "now."

You were just asking if your sentence below grammatically make sense.

'If not, I would like to sit down with her before the meeting to quickly acclimate myself with how things are presently being done'.

Of course, it does make sense and I clearly understood it. It's just a matter of taste.

Since business letters are written concisely and simply worded, you can reconstruct the sentence like this.

If not, I would like to sit down with her before the meeting, to familiarize myself on how things are currently undertaken.

Actually, it matters to me how you would like your thoughts to reach the receiver.

If not, I would like to sit down with her before the meeting, to familiarize myself on how things are currently undertaken.
That's even worse!

No comma after "meeting," and who says "currently undertaken"?

If not, I would like to sit down with her before the meeting to find out how things are being done.