When I was running all task+ I struggled to remember which tasks I did and would often delete runs that missed a task or did the same one twice. I really don't think the routing differences are significant enough for it to save much time.

No, the routing differences are only CURRENTLY similar because not enough experimentation with having all the tasks unlocked has been done, otherwise, routing could be vastly different between the two categories. They need to be separated.

I meant, can I submit a run for all tasks+ but without the tasks unlocked so I dont have to worry about forgetting tasks

As long as you did all the tasks it really shouldn't matter since tasks+ only gives an advantage in the regard that the player can choose which tasks they can accomplish first, and gives them access to nearby tasks quicker since you can just jump right into whatever. Doodletones does make a good point though, your run would be very poorly optimized in comparison to an individual who took the time to figure out what is the fastest way to get it done. I'd say just get a tracker where you can simply click when you're done with something, it can easily be done on a smartphone with the timer apps installed on default, at least on android.

If you do manage to beat the best record for the task+ runs with a normal run I would be impressed, but I am doubtful it would stay up when somebody took advantage of the category rules, making the submission somewhat obsolete.