C (gcc), 70 bytes

o(s,a)char*s;{for(a=0;s[1];s++)a|=s[1]-*s&64|*s-s[1]&32;return a!=96;} 

Try it online!

C (gcc), 70 bytes

o(s,a)char*s;{for(a=0;s[1];s++)a|=s[1]-*s&64|*s-s[1]&32;return a!=96;} 

I was hoping to find a shorter solution based on a recursive function, but it didn't work out due to the output requirement. So here's an imperative approach. At least, C's operator precedence works nicely for the inner loop statement.

Try it online!

C (gcc), 59 bytes

o(char*s){s++;return!*s|!s[1]||(s[-1]-*s^*s-s[1])>=0&o(s);} 

Assumes signed char.

Try it online!

C (gcc), 70 bytes

o(s,a)char*s;{for(a=0;s[1];s++)a|=s[1]-*s&64|*s-s[1]&32;return a!=96;} 

Try it online!

C (gcc), 60 bytes

o(char*s){return!s[1]|!s[2]||(*s-s[1]^s[1]-s[2])>=0&o(s+1);} 

Assumes signed char.

Try it online!

C (gcc), 59 bytes

o(char*s){s++;return!*s|!s[1]||(s[-1]-*s^*s-s[1])>=0&o(s);} 

Assumes signed char.

Try it online!