Since you're using >>, which means append, each line of output from each instance will be appended in the order it occurred.

If your script output prints 1\n through 5\n with a one second delay between each and instance two is started 2.5 seconds later you'll get this:

1
2
1
3
2
4
3
5
4
5

Since you're using >>, which means append, each line of output from each instance will be appended in the order it occurred.

If your script output prints 1\n through 5\n with a one second delay between each and instance two is started 2.5 seconds later you'll get this:

1
2
1
3
2
4
3
5
4
5

So to answer your question: No.