You might give it a try. There are various reasons why it goes into recovery mode. Obviously there's something wrong, and it can't really self-diagnose what's wrong. The most serious (for recovering data) would be corruption during an iOS update. If that's the reason why, then it should be pretty easy to get the iPhone working again by rebuilding iOS using a Mac or Windows PC. But if that's the case, there's no practical means to recover the data.
I've heard of a few cases where a wet iPhone came up in recovery mode. I suppose in those cases there might be something blown that's allowing partial functionality enough for the display to work. In many cases a wet iPhone will just be dead. But if one is desperate enough, the processor, flash memory, and other security components are still intact, it might be possible to place that in a donor iPhone to extract the data. Or it might be possible to just fix whatever might be damaged enough to recover the data.
You can research who does hardware repairs, and perhaps look for a company that doesn't charge without recovering any data. We can't recommend anyone specific here.