Note that I am currently an undergrad.
One month ago, one of my professors agreed to let me work on a research project with him. After a few weeks of not hearing anything from them, I emailed the professor asking about the project (1.5 weeks ago). He replied saying that he would be contacting a collaborating researcher (at a different institution) in the project within two days and can discuss a roll for me with them. Based on the language of the email, it seems that he had been waiting for me to email him. He said that he would contact them in two or so days, so 1 week ago, and then get back to me.
I still haven't heard back from them and so I am wondering if it is inappropriate for me to email the professor and ask about the project a second time? (note that based on the current situation, we can only email each other and not talk in person). I realize that many times going through such a process can be a bit slow but I am in a position where a recommendation letter from this professor (who is well known in their field) would be significant, as he could then talk about my academic experience with him as well as my research experience with him.