Yes, it can. The variables that are used to keep track of everything are just expanded into an extra array-dimension, and that extra dimension contains values at 0 (current status), 1 (player 1's turn after draw one turn ago), 2 (player 2's turn after draw one turn ago), 3 (player 1's turn after draw 2 turns ago), and 4 (player 2's turn after draw two turns ago). Each time a turn's initial draw is made, the new instance is recorded and everything already in 1, 2, and 3 drops down one layer. Players would only experience a slight (read: fraction of a second) delay after every turn's initial draw, the storage space to keep track of all this is minimal.
One great reason to consume all
is to avoid having to store more than two turns ago - although it IS theoretically still possible to cast two of these in one turn. You have to have had four Supernovas and one Time's Arrow two turns ago after the draw, and drawn a second Time's Arrow any time from then until the first casting.
The only way I can see to avoid this recursion would be to increase the cost (both unupped and upped) to at least 15 - this is more than 7 supernovas can refund. If you factor in Electrum Hourglasses and luck, it gets even CRAZIER. Plus since the reversion is two turns, you could cast Time's Arrow on back to back turns, totaling 3 turns of rewindage...
I've been hashing this card around in my brain for weeks, and I did think of these possible issues. At one point, my idea changed to a permanent, to introduce both 1) summoning sickness, and 2) an early warning for opponents. I might still do that. Heck, this is an Arrow we're talking about... I also thought of making it a weapon.
Tucking: sure, but there are significant differences:
1. Permanents are totally unaffected.
2. The amount of turns a player can be sent back is fixed, while the Gate of Remembrance could send you back massively.
3. Hand is also affected, meaning some creatures played may actually be "partially-rewound" into the opponent's hand. This also means you may allow your opponent to duplicate a few of his permanents or use a spell again.
I put a LOT of thought into this before I posted. There are a few hairy issues to be cleaned up somehow - like the programming end of things, and reverting more than two turns - but I believe this can be balanced well enough to be interesting and strategic, but not massively powerful.