For typical uncontrolled airports which have instrument approaches, they are usually in Class G airspace from the surface to 700’ AGL. In this airspace, yes, you can - at least from a regulatory perspective fly in IMC without ATC clearance, provided your remain clear of controlled airspace.
In order to fly a cleared IFR flight plan, you would have to depart into uncontrolled airspace prior to climbing into the Class E shelf above the airport. Typically, IFR departure clearances from uncontrolled airports contain a time window in which you must be airborne and in contact with a regional departure control or ARTCC by eg “Clearance void 30 minutes from now”. Basically, in doing so, ATC have given you a block of airspace which you have use of for a small time window in order to get airborne and join ARTCC on your cleared flight plan. Once you have departed the uncontrolled airport on CTAF, you would immediately go over to your assigned departure control frequency and report in. The controllers would thence take over and direct your flight.
A typical IFR clearance from a untowered airport would be something like as follows:
Mooney Three One Two Seven Zulu, Atlanta Approach, Cleared IFR From Cartersville Victor Papa Charlie To Charleston Charlie Hotel Sierra Direct NELLO Then As Filed. Climb And Maintain 5000, Expect 11000 Five Minutes After Departure, Atlanta Departure Control Is On 121.00, Squawk 2477. Clearance Void 30 Minutes From Now.
From the moment you copy the instructions and the controller acknowledges so with a “READBACK CORRECT”, you now have thirty minutes to get airborne, on a course direct to the NELLO fix and contact Atlanta Departure on 121.00 or the clearance becomes invalid and you must request a new clearance to do so. If there are low clouds between you and the time you switch over to departure, so be it, you’re going into IMC. Usually, though, it’s best once airborne and cleaned up, to immediately go over to departure control as quickly as you can.
Another example of IFR flight in Class G is flying an instrument approach into an uncontrolled airport. Once you descend below the Class E shelf, the controller hands you off to CTAF and you continue on in uncontrolled airspace. If you’re flying an ILS approach down to minimums, that may well be another 400-500 ft descending uncontrolled in IMC before you either break out and land or go missed, thence rejoin center to report a missed approach.