We may be rather out of our depth here: given that the transport police were called, do you know if your son is being prosecuted by the railway, or by the police (which would presumably mean the Crown Prosecution Service (CPS))? If it's the police/CPS, I'm not sure that anyone here knows whether they are prepared to negotiate out of court settlements.
If it's the railway who are bringing the prosecution (and I think this is more likely) then an out of court settlement is possible, but is by no means guaranteed. If there is time before the hearing, then your son should write to the railway, accepting that they were in the wrong, explaining what they will do to avoid problems arising in future, and asking if the railway would be prepared to settle out of court for the cost of the railway ticket that he should have had plus any costs that the railway has incurred. The letter should be apologetic, courteous and short (someone has to read it!).
If the hearing is close - or if the letter doesn't come up with a positive response - then from time to time we hear of people managing to settle literally at the door of the court. Your son will need to arrive early, ask the court staff to point them towards whoever is prosecuting for the railway, and try to discuss to arrange a settlement there on the day.
But what if this doesn't work, your son does appear in court and is found guilty? In that case, he will be punished and may have a 'criminal record'. In our experience, fare-dodging (when that's the only charge) is invariably punished with a fine rather than with prison. But this case is aggravated by being abusive to the staff. Realistically, unless there's physical contact as well (which could be assault or a more serious charge) I cannot see that abusive language would lead to imprisonment. So if the matter goes to court, your son should expect a fine, plus compensation (the train fare) plus prosecution costs, plus court costs.
What about a 'criminal record'? There's a piece of legislation called the 'Rehabilitation of Offenders Act' which lays down that conviction for relatively minor offences shouldn't ruin offenders' lives for ever. It does this by ruling that offences become 'spent' after a fixed period of time, and after that period there's no need to mention them in most circumstances. There are, however, some circumstances when they don't become spent: these tend to involve times when someone might be in a position of great trust or power over someone else or their money - which means things like being a teacher, nurse, doctor, careworker and so on (a position of trust or power over someone) or a lawyer, accountant, a banker or someone working in finance, or someone handling cash in a shop (control over other people's money). In these cases even 'spent' convictions may have to be mentioned.
In terms of railway convictions, if your son is convicted under the railway byelaws (most likely byelaw 18 for the ticket and byelaw 6 for the behaviour) then my understanding is that the conviction becomes spent immediately - that is, he will be under no obligation to tell anyone about it. I also gather that in general byelaw convictions aren't included in the DBS system. If the conviction is under the Regulation of Railways Act, then I understand it to take a year for the conviction to become spent.
So having a 'criminal record' may not be an issue - even if your son does end up in court. But even a criminal record - for one offence - may not be a disaster. In our experience, many employers understand that people make mistakes from time to time. And one incident (even one incident where your son lost his temper) isn't a problem. What may be a problem is repeated misbehaviour - and employers can see trying to cover up something like a conviction as repeated misbehaviour.
So I would suggest that your son tries to find out beforehand what the impact of a conviction might be. If he is in a union at work, then they would be good people to ask. If not, then he may want to see if he can ask a colleague who he can trust not to pass this enquiry on to management (and to give him a sensible answer!). It might also be worth having a look at his contract / terms and conditions of employment to see if that gives a clear answer.
Hopefully this will provide an answer that reassures him. But since employment relies on trust between employer and employee, in most cases I think that if he is convicted he would be well advised to come clean to his employer. Whatever he has found out beforehand will hopefully help him decide whether to approach this as just passing information on to his employer in a spirit of openness, or as throwing himself on his employer's mercy.
In general, I would not expect one railway conviction to be career-ending - and probably not job-ending either. But your son should check carefully.