As mentioned in the thread SQL structure question, I don't know of any reason why you can't. As long as you allow MYSQL to generate the id's it should be in order.
The only thought I have as to why you wouldn't want to only have the id to keep track, is in an instance where you need to combine the data with another table and still keep track of the order. In that case having a DATETIME column would allow you to combine and regenerate the order.
You'd order the data by datetime and id for both tables. The id's will make the sorting somewhat arbitrary between tables, but each tables data should be in the same order.
If the auto_increment column cannot be used then the only way as far as I know to order the data would be to manually make your own counter.
LOCK table INSERT based on maximum + 1 UNLOCK TABLE
For those wondering why not use the DATETIME column or a more precise time value to keep track. The problem is that even when locking the table it may be possible that two rows get the same time value. ie the LOCK, INSERT and UNLOCK happens fast enough for them to still get the same value