its not that simple... there are 4 scenarios.. not one.. dont confuse one for the other
1.
if only
some miners upgraded to 2mb (miner c) and A and B were regular <1mb block limits this would happen:
inshort, C(large) blocks would get orphaned
2.
if 2mb implementations(classic or xt or BU) only communicated to miner C and totally ignore miner A, B.. then 2mb imps and C would have their own unique data (fork/altcoin). and segwit would get data from A,B happily and just drop C.. so A,B and segwit would share data.. 2 chains not talking to each other..
3.
if ALL miners upgraded, but there was a mix of segwit and 2mb imps.
then the miners would all have the same chain data, 2mb imps would have the same data... but segwit would be left behind missing a few blocks it deems not compatible. in short segwit wont be able to sync with the network as its left way behind and their chain is missing a few links
4.
if no miners upgrade.. and only users do.. then users can still get 1mb blocks as there is nothing stopping them.. the rule is anything below 2mb so even under 1mb is still valid to a sub 2mb node
and they are ready for any surprises in the future as the extra setting change is just sat there an unused buffer,..
summary.
scenario 1 is acceptable as it will regulate itself,,, orphaning off when needed is bad, but it can work..(eventually C miners would downgrade to <1mb to avoid ophans and loss of revenue.. si it works out in the end)
scenario 2 and 3 are not good for the community as a whole..
scenario 4 is acceptable. because miners will still be producing <1mb blocks so the whole community still receive the same data.
but as the OP asked.. its the miners that can cause scenarios 2, 3 if they upgraded, which is not what the community want until its ready to happen
but if there was a scenario 2 or 3.. then the OP can import his private key into a service he wanted to use with funds he already had to play around on that chain..
the problem.. lets use scenario 2 for instance.
if he received funds from someone on 2mb imp chain.. it would only appear on 2mb imp chain and he would need to find a service that uses 2mb chain.. same for segwit.. if he received a segwit transaction while there was 2 chains.. then that new funds would only be on the segwit chain..
but if he had funds cold stored before the fork.. then they can be used on both chains. as they existed on both chains when the data use to be the same chain