Bash: If/Else statement in one line

There is no need to explicitly check $?. Just do:

ps aux | grep some_proces[s] > /tmp/test.txt && echo 1 || echo 0 

Note that this relies on echo not failing, which is certainly not guaranteed. A more reliable way to write this is:

if ps aux | grep some_proces[s] > /tmp/test.txt; then echo 1; else echo 0; fi