Is the word acaso the same in Brazilian and European Portuguese?

Yes

The meaning, grammar, and spelling of "acaso" are identical in both Brazilian and Continental Portuguese. The only difference is pronunciation. In Brazil, the vowels are generally more open and the rhythm is more melodic (syllable-timed), whereas in Portugal, unstressed vowels are often reduced or almost swallowed, resulting in a more stress-timed rhythm.

Brazilian Portuguese Examples

1. Por acaso você viu meu celular? (By any chance did you see my cell phone?)
2. Foi apenas um acaso encontrar você aqui. (It was just a coincidence to run into you here.)
3. Por acaso você tem um minuto para falar? (By any chance do you have a minute to talk?)
4. Nada acontece por acaso neste mundo. (Nothing happens by chance in this world.)
5. Eu encontrei ele por acaso na rua. (I ran into him by chance on the street.)

Continental Portuguese Examples

1. Por acaso viste o meu telemóvel? (By any chance did you see my mobile phone?)
2. Foi apenas um acaso encontrar-te aqui. (It was just a coincidence to run into you here.)
3. Por acaso tens um minuto para falar? (By any chance do you have a minute to talk?)
4. Nada acontece por acaso neste mundo. (Nothing happens by chance in this world.)
5. Encontrei-o por acaso na rua. (I ran into him by chance in the street.)