Your EOS Rebel T3i/600D will not be able to shoot video if the shutter is inoperative. The shutter must open and remain open in order to use the T3i to capture video. But your shutter may very well last far longer than 100,000 actuations. Canon stopped releasing shutter life ratings for the EOS Rebel series with the EOS T1i/500D, which had a rating of 100,000 actuations. So technically, there is no shutter life rating for the T3i/600D.
A shutter rating on a camera is like a mileage rating for a car. It is what one might expect to be the approximate durability of the item, but it is neither a guarantee nor a hard barrier beyond which the device will no longer function.
If one buys a car with an expectation that it should be good for around 300,000 kilometers that doesn't mean there's no way it would last beyond 300,000 km. It might go for 500,000 km before needing any major repairs, or it might blow the engine after the first 1,000 km. The same is true of a camera and its shutter: There's no guarantee the shutter will fail immediately after the 100,000th click. It may last for over 1,000,000 actuation like at least two Rebel T3i/600D examples have, or it might have failed after less than 100 clicks.
Here's a chart with a distribution of T3i shutter statuses (working or failed) at various points along the way from 0 to 2,000,000 actuations as self reported to Oleg Kikin's Shutter Life Database (please note that someone is statistically far more likely to report a camera that has failed to such a site than to report one that has not failed). Of the 560 total cameras reported, 145 of the shutters had failed at the time of the report and 415 were still operable.
Only about two-thirds of the 560 EOS T3i/600D cameras reported to the database have lasted through your current 92K actuations. Other than early failures within the first 2,000 clicks that were very likely coverable under warranty due to a factory defect, one has to go beyond 500,000 shutter actuations to find a range where more failures have been reported than cameras that still have working shutters.
For more about shutter life ratings and what they mean, please see:
Does the Fujifilm X100 have a limited number of shutter actuations, similar to focal-plane shutters?
How significant are 14000 shutter actuations for Canon 6D?
Did shooting in burst mode wear out my shutter?
How many actuations are "too many actuations"?
For how Live View and capturing video is related to activating the shutter, please see:
Does live view increases the number of shutter actuations?
Does every frame of video (or live view) on a DSLR count as a shutter actuation??
Does shooting video decrease the life of a DSLR more than taking photos??
And in the case your shutter does fail, it is a comparatively cheap repair for most DSLRs.