Write Modubs register after (re)connect

Only “kind of”, for Modbus.
Let’s look at how Modbus works.
openHAB is a Modbus master, your PLC is a slave.
A Modbus slave never talks unless it is spoken to. Your PLC cannot announce "here I am’.
So openHAB can never know if a slave is turned on or not unless it tries to read something from it, polls it.

So you are going to have to poll your slave in some way.
Probably you have “normal” read polls of various registers that will do for this purpose.
If the read poll fails, because the PLC is switched off, it will generate a timeout error at openHAB’s end.
The read error will cause openHAB’s Thing to go OFFLINE with an error.
The read poll will continue to be carried out, logging new errors every time.

If the PLC is eventually switched back on, presumably the read poll will then succeed? I don’t know, does it work before you have done this watchdog write business??
If the read poll does work, openHAB will change the Thing status from OFFLINE to ONLINE.
A rule can look for that change, it indicates your PLC has come online again.
That rule can do whatever write it is that you want.

If you have other Modbus devices as well, beware that continual errors on one device can badly effect performance of any remaining devices.
You probably ought to understand this post about the effects.
It also shows an example of a rule acting on Thing status changes.

You might also have to think about what you would like to happen if some other kind of real error causes your Thing to go OFFLINE.