If you do, according to a report in the Sydney Morning Herald, the resulting bureaucratic tangles will drive you batty. Here's an excerpt.
When your passport and valuables are stolen in Thailand - including all your cash - the first thing the victim must do is pay money. That's right, you've been robbed of everything you own, now it's the policeman's turn.
Police reports (for insurance) don't come for free, I discover halfway through reporting the crime to an awfully young trainee policeman. No money; no report. So I borrow 240 baht ($7.50) off the nearest backpacker (a feat in itself) and finish the process.
. . .
I explain to the woman at check-in at Koh Samui airport that I'm flying to Bangkok to replace the passport I had stolen. I even show her my 240-baht police report. "No photo identification, you can't board the flight," she says. I reason with her. Then I beg. She calls for the airport manager. "Sorry sir, without photo ID, you can't get on this flight."
I rip my flight itinerary into a thousand angry little pieces and make my way to the harbour, where I begin a journey involving ferries, trains and buses that will take more than 12 hours (the flight time was 65 minutes).
. . .
The next morning at customs there's a problem; they need to see a Thailand entry stamp on my passport. I show them my 240-baht police report. I cry a little, I tell them I just want to go home. It's no good.
Instead I'm frog-marched to a stark room where six customs officers watch a World Cup qualifying soccer game on TV. The game's obviously an important one because no one wants to leave it despite my teary protests that my flight's about to board.
There's more at the link.
After reading that, I think I'll do my best to avoid the place . . .