Good for you Shauna!
It's allays exiting to see "new stuff" coming up!
Not sure,... if it was me I wouldn't, because fruits need all the sunlight they can get, it makes them taste better, so cheesecloth would shade it too much I think?
What I have done on my sweet cherries, cover with one or two layers of bird netting, these have large holes and let more sunlight in.
Konrad

Shauna, congratulations on having some cherry plum fruits on your shrub! I know how you feel. The neighbour's apricot tree is full of fruit this year, and several branches hang over into my yard. I can't wait! (There have been a few apricots on my side of the fence, in the past, and they've been small but delicious. Unless we have a severe hail storm (knock on wood), this will be a bumper crop!!)

I don't know if cheesecloth will sufficiently protect the fruit. I found one website (that's mainly about apples, but does talk about other fruit) that recommends using paper bags. Read the first part of the article, and see what you think.

Good luck!! Bet you can taste them, already!!

Here is a link that might be useful: Protecting fruit