You may be able to use united.com Easy Check In to place yourself on standby for the earlier flight. The only reason it might not work is if the Easy Check In will not process it due to the international segments. If you then somehow miss the earlier flight you'll still have your confirmed seat on the later flight.
If you misconnect you can always ask for a hotel voucher, or maybe they will offer one. The ORD Hilton is the best hotel as it is connected to the terminal complex and you don't have to take a shuttle. You can specifically ask for the ORD Hilton, and if they have it they likely will give it to you.
The official policy on hotel vouchers due to weather/atc is they are given to 1K/UGS status members and people in C/F. People with other status don't technically get them, though in the end the final decision rests with the agent you are dealing with. So you may be able to talk them in to it depending on your skills of persuasion and the agent you get. Of course if you don't like the answer one agent gives you, another agent may give you a different answer, and a third agent will probably give you a third interpretation

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If your flight cancels mechanical, or there is some other unusual circumstance, then typically hotel accommodations are provided regardless of status.
I wouldn't worry about it at all, unless it is critical that you be in your final destination that night. Like you have some very important appointment you must deal with that day. If thats the case, given the system, you would probably have been better off leaving the intl destination a day earlier. But other than that (a critically urgent business or personal appointment), don't worry about it and enjoy the adventure

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FYI I misconnected a couple weeks ago at ORD, and actually enjoyed myORD Hilton stay courtesy of UA. The world didn't end because I arrived 1 day late at my destination.