can I get off the train and then continue

if I buy a train ticket from Tokyo to Kyoto, can I get off the train in, say, Hikone and then get on the train to proceed to Kyoto?

I think this is possible.

No, you cannot do this unless you pre-organise it and book the appropriate tickets.

Note that Hikone is not even on the Shinkansen line so if you want to visit Hikone you would probably have to switch from the Shinkansen at Maibara and then take a local line train to Hikone.

You can either buy two completely separate tickets. Tokyo - Maibara, and then Maibara - Kyoto. If you want to save a little bit of money and you don't find the following too confusing then you can buy the Base Fare ticket for Tokyo - Kyoto and then buy two separate Shinkansen Supplements for Tokyo - Maibara and then Maibara - Kyoto.

You may find things a lot easier with a JR Pass as it is much easier to hop on and hop off so if you want to post your itinerary day by day with dates and days of the week it will be easier to see if a JR Pass would pay off.

Enjoy your trip!

Pardon me.
I assumed you have a JR pass.
With it, you can and I have tried.
It may be better to reserve the seats in the 1st train and then the next train for your onward journey.
But do you stop for sightseeing?
If so, you may need to allow sufficient time for the next train.

You can get off the train. You cannot however, go through the gantry.
Maybe to visit the station store or use the toilet. Or maybe take photos of a landmark.
E.g. Castle, Fuji mount

I am not confident, so correct me if I am wrong.

Basically you can get off and go out of the station along your way to the destination as long as you bought normal JR ticket (not special ones like Puratto Kodama etc.) and the traveling distance is more than 100 km. And of course you can re-enter the station and continue to travel. Each ticket has own valid dates, so it must be within this period.

In this case, Tokaido Shinkansen is considered to be identical to the Tokaido main line including Biwako line on which Hikone is located.

So if you want to get off at Hikone and then explore the town, you should buy normal ticket to Kyoto and Shinkansen ticket to Maibara. Change train at Maibara (and maybe at Nagoya also) and go to Hikone. Note that you can not backtrack to Maibara, since your normal ticket is stamped in Hikone. Just ride on Biwako line train to Kyoto.

PS: GC3, long time no see. Happy to see you here!

A gantry is a kind of a crane, used in ports to load containers, or, on roads and railways, to built bridges, elevated tracks etc.

You mean a train station GATE don't you?

if you have a shinkansen ticket, you CANNOT leave on the earlier station and come back on the same ticket. You will loose the ticket at the ticket gate and if you ask the train station staff, they will tell you it is not possible (tried that in Osaka, they didn't let me even to a shop outside the gates).

You can buy a combined ticket that will allow you to get off on previously chosen station, so you can by a ticket from Tokyo to Hikone and from Hikone to Kyoto (if you use shinkansen, you need to transfer at Maibara). Mind, that the price probably won't be more expensive even if you have a stop on the way.
If you use the regular JR line in Kansai, you can buy a cheaper ticket in one of the cheap tickets selling point outside the station. They will combine a couple of tickets to make it at least 10% cheaper. For example, if you want to go from Hikone to Kyoto, they will sell you a ticket from Hikone to Oumihachiman, from Oumihachiman to Ritto and from Ritto to Kyoto. You get 3 tickets in total, so you can have a break at Oumihachiman, for example.

regular fare = Tokyo - Kyoto
limited express fee = Tokyo - Maibara.

Tokyo - [shinkansen] - Maibara - change a train(they take limited express ticket) - Hikone.
show your regular ticket(keep your regular ticket) at the gate.
sightseeing.
re-enter with your regular ticket (Tokyo-Kyoto). take a Shin-Kaisoku train (no extra fee,generally run every 30 mins) bound for Kyoto direction. your regular ticket will be collected at Kyoto.

Wait! All Yes All No both are quite wrong just depend on your ticket type.

Hikone is not Shinkansen[新幹線](high speed track) stop station
http://en.biwako-visitors.jp/access/ (Shinkansen : thin orange color line)
So if buy a "regular" oneway ticket for Kyoto ...
A) arrive Kyoto[京都] by Shinkansen first then return to Hikone[彦根]
and back by JR local train is No! (invalid)
B) get off Maibara[米原](or Nagoya[名古屋] and more before) by Shinkansen first
then to Hikone and to Kyoto(no back/return) by JR local train is Yes!
(within vaild 4 days/401-600km. Tokyo-Kyoto: 513km)

But if buy a "Japan rail pass(not regular)" also Yes!
if buy a "Puratto-kodama for Kyoto(not regular)" is No!
by special ticket rules.

*)
This "local" means "local line[zairaisen：在来線]" (vs Shinkansen line)
JR local line operating all station stop "local[futsuu：普通]
and some stations skip type as "rapid[kaisoku：快速]".
JR means rail comany name.(JR-East.JR-Tokai,JR-West and more)