I'm currently a CA-2 and during internship, had one month of ICU and one month of CCU. Use these months to build a knowledge of sick patients' issues, since you will find yourself taking care of them in the OR. You'll learn how to organize all their pathology into organ systems, especially cardio-pulmonary for anesthesiology. Also get familiar with ventilator management.
I did a few lines during these months, but those will come to you with time. In anesthesia residency, you will do a ton of lines during cardiac rotations and anytime you get a sick, crashing patient to the OR (assuming they haven't already been lined up). More importantly, it's nice to know why they are crashing so you can anticipate your next move. This is all obvious stuff, but this is why it's important to do ICU during internship. Once you rotate in the ICU as an anesthesia resident, you'll know how to deal with acute issues with more ease, but your foundation during internship will also help.
As for the anesthesia month, I did one, but it was kind of unorganized and I didn't get to do as much as I would like, but again, your procedures will become easier once you've done enough of them. If you do get a chance to do an anesthesia month, go for it and get a head start on intubations, spinals/epidurals, lines, etc. As a med student and intern, one thing I miss was the freedom to go from room to room checking out different cases/procedures.