Yes. Saat ini = [at] the moment.
Sekarang = now.
I think the usage whould differ about like this:
"I want to go to the cinema. Do you want to come?" - "I'll be with you in a sec, but I eat an egg now." (saat ini = it's only gonna take a moment)
"Lucas, you haven't done your chrores yet!!" - "But mooom, I'm eating an egg now!" (sekarang = no indication, how long the action is going to take)