Yes, frequency matters.
A transformer is a coil of wire.
A coil has inductance.
(almost all circuits have inductance, but a coil of wire typically has a more inductance than a say a straight wire. A coil kind of concentrates inductance. I am sure that that there are many books and thesis about induction but if you just google it you will find info at many levels)
One of the properties of inductance is that can cause current to lag behind voltage. This current lag is frequency dependent for a particular inductance level. Inductance is measured in units called "henry".
The phrase "current lag is frequency dependent" really means it acts like a filter. This filtering action is called impedance. All this stuff can be described by algebra. A wire made filter will turn unwanted energy into heat. If you feed an xformer or coil with a freq. that it filters (high impedance) and you have a lot of current with respect to the wire size of the coil you will get a lot of heat FAST. From what you describe you may be dealing with 3000 watts. That could mean a LOT of heat, so safety is of major concern.
You said you were going to pulse the xformer input. If you are using rectified ac at the freq. the xformer is rated at no problem. (use full wave rectification so you get full power out) However if you are using any kind of square wave there is a problem.
A square wave takes very little time to reach it peak voltage. Compared to a sine wave a square wave reaches it's peak voltage almost instaneously and that is the way a coil will see it too. So that current lag behind voltage will eat away at the rising side of your square wave. You will loose power at the output of you xformer and generate heat.
I found home made plasma cutter stuff on u-tube. I did not watch all the videos but, I already have a plasma cutter.
Since I don't your technical level or what the end use for your cutter is, I thought I would drop this suggest If your intention is to cut ferrous metal you may want to consider getting an oxygen acetylene torch. You don't need to plug it in and you can weld with it too.
Have fun