They wouldn't need a probe, just the funds. There are manned submersibles that will go to the bottom of the Pacific. Limiting Factor, the name of the submersible built by Triton Submarines and properly certified, has gone to the very bottom of the Marianas Trench, at a depth of 35,839 ft. The explorer Victor Vescovo has done this dive eight times, so the examination of that aircraft wreckage would be well withing range.
Also, James Cameron dove down with the Deep Sea Challenger sub to the bottom of the trench and poked around down there for several hours. His dive was the first solo effort to go down that far.