Yes -- although "without amounts or scripts" gives a clearer idea of what the transaction graph will look like: every output is a uniformly random curvepoint. This story is actually quite a bit better than Bitcoin where there are "addresses" which are often public and often reused.
In general, finding a p2p layer that hides the original, unmerged transactions, seems difficult. Initially I had thought it would be possible for "passive merging" where nodes would just aggregate all the transactions that they saw, taking in unmerged transactions and outputting merged ones. This appears to be very fragile: consider three nodes which each have a transaction, say
C. The first node publishes
A, then the second and third latch onto it simultaneously, outputting
AC respectively, and now only one of
C can be confirmed. Observe that this happens even without any adversarial behaviour, and happens even if merging is only done by some special set of "masternodes".
The problem ultimately comes down to the fact that with OWAS, conflicting merges (transactions with intersecting input sets where neither is a subset of the other) look identical to conflicting
transactions (double-spends). So "unifying"
AC to get
ABC, which is the desired network behaviour, is just as hard as "unifying" a double-spend. Which, to be clear, is "doesn't even make sense" levels of difficult.
It may be possible to have a p2p layer that does interactive merging somehow, which in Mimblewimble could be made much simpler than Coinjoin in Bitcoin, so that transaction creators have control over what other transactions their transaction gets merged with on the wire. Miners would then drop the signatures or whatever was needed to enforce interaction at the p2p layer and just merge what they got. This might be sufficient to stop the creation of accidental conflicts, but you then have to worry about adversarial behaviour.
It would be possible for users to directly communicate transactions to miners; for a given transaction they'd give a different version to every miner so that nobody but the miner who created a
block would be able to tell what the original transactions in the block were. Absent collusion this would erase a lot of the transaction graph from any specific adversary's view, although it would enforce miner centralization which I find very undesirable.