Yes the monitor can be attached. It can be either ECG (electrical) or a finger pulse monitor. Both work fine.

ECG monitors do have problems with MRI, because the scanner generates an absolute ton of electrical interference which messes up the waveforms.

The waveform is also distorted because when you move something which conducts electricity (like a wire, but also blood or heart tissue) in the presence of a magnetic field, that movement generates electricity. The electricity generated by the moving blood and heart muscle can mess up the trace - it's still good enough for timing and syncing up the scan - but it doesn't look like the trace you get in textbooks.

Heart monitors are absolutely a hazard if used with MRI incorrectly. Obviously, you wouldn't use one with any magnetic parts. However, because of the enormous electromagnetic fields generated by the MRI scanner, there can be all sorts of weird effects with wires and metals. So, it's very important that the correct monitor and sticky electrodes be used. Electrodes with too much metal in them can get hot and burn the skin. Wires which are too long can pick up interference from the scanner, concentrate it and direct it into electrodes, also burning the skin. There are special monitors and electrodes designed specifically to withstand these effects and absorb the energy safely so as not to burn the skin. These monitors also contain special electronic filters to try to filter out most of the interference produced by the scanner so that the waveform isn't completely swamped by just static and interference.