Yes. There is no inherent problem doing that. It won't filter the DC as well though. You are just changing the power supply topology. A choke is not "required" for a capacitive pi filter, just a resistance in that place in the circuit. BTW, since the power tubes get their voltage off of the first power supply node (before the choke), this really won't make much difference in the squishyness of the power section of the amp.
That being said, you can try some other things that will let you keep the superior filtering of the choke & add some spongieness to the feel of the amp.
1.) Just add a resistor in series with the choke (100 - 1000 Ohms maybe?). You get to keep the choke for good filtering but still add some "sag". However, this will still not affect the power tubes (as noted above).
2.) Add some low value, high wattage resistors in series with the rectifier (either on the AC side or directly following the dioides, I don't think it matters much). This is a poor man's tube rectifier simulator. The voltage drop across the resistors will change with current draw & affect the voltage rails of the entire amp, including the power section, similar to a tube rectifier. Start with something small (like 22-47 Ohms) and work your way up from there until you get the feel you like. Keep the choke in the circuit.