Nesse caso sim Laís, mas o begin costuma ser mais formal, inclusive no dicionário Cambridge explica outros casos de quando utilizar um ou outro.
Begin or start?
De English Grammar Today
We can use the verbs begin and start to mean the same thing but begin is more formal than start. Begin is an irregular verb. Its past simple form is began and its -ed form is begun:
When did you begin learning English?
The meeting didn’t start until 9 pm.
We use start, but not begin, to talk about machines:
Press this button to start the printer.
Not: …to begin the printer.
The lawnmower won’t start. (this means that it doesn’t work)
Not: The lawnmower won’t begin.
Start, but not begin, is used to talk about creating a new business:
She started a new restaurant and it’s been going really well.
Not: She began a new restaurant …
Fonte: http://dictionary.cambridge.org/pt/gram ... rt?q=begin