If the two paths discovered by AOMDV from the source to the destination are node-disjoint, they can be used for simultaneously sending packets, if not, then they cannot be used for simultaneous data transfer.
For sharing traffic, node-disjointness among paths from a given source and the destination is necessary. However, from the viewpoint of fault tolerance only, it may not be necessary. In case of AOMDV, it may find paths that are link disjoint. These paths provide fault tolerance but not traffic sharing. To find node-disjoint paths one needs to develop one's own protocol.
So, current multipath routing protocols for MANET like AOMDV, AODVM, SMR, MP-DSR, CHAMP, ... just maintain some backup routes by default? so why we call them multipath!
Should we modify their codes in simulators to transmit simultaneously?
Yes. Most of them discover alternate backup paths so that if current path fails due to node and/or link failures, traffic is directed through an alternate path. Their strategies for identifying alternate paths are different. The paths discovered by most of them might not be node-disjoint. The objective behind most of them is fault tolerance rather than traffic sharing.
If someone wishes to identify node-disjoint paths then one has to adapt the protocol in such a fashion that it always returns multiple node-disjoint paths between a given source and a destination. I suggest that you may have a look on the following of our paper