The processing time according to the CBSA as of January 28, 2020 is 39 business days. This is a little more than it was when I was approved in August 2019, when it was 25 days, which is exactly how long it took me As far as I can tell, it's quite accurate, however, no one can tell you exactly how long you The application will take.
As an anecdote, my mother recently submitted her application and did not receive conditional approval in a short period of time, so it does not appear that the waiting time has diminished since when I requested it.
Since there is a maximum of 45 business days until the end of March, the probability of obtaining conditional approval and scheduling your interview is very low, although theoretically possible. However, since your ability to use Global Entry is based on your passport, not the NEXUS card, you can use it immediately after approval in your interview, so if do If you are conditionally approved and receive an interview, it would be good to go.