Am i stupid or is it that simple?

Hello! I'm new here.
Three days ago i bought a 50mW Noname(tm) greenie.
Having searched the web for explanation of the SHG phenomenon i thought of a theoretical question:
If the IR LD emits 808nm which is transformed into 1064nm and then doubled by the KTP crystal to 532nm, what will happen if the first crystal is removed? What if LD shines a beam of 808nm through the KTP directly? My guess is that it'll double the frequency to 404nm - Hey! it's visible violet!
Of course, i don't wanna try modifying my laser in any way, but i'd like to hear if such a thing is possible.
(ow, i forgot- i live in Israel and it's quite hard to get a powerful laser here. i contacted some piratic sources, but i was lucky to find them.)

No it's not. I did some looking into this a while ago. KTP does not double 808nm at anything like worth bothering with efficiency - you might get 0.001mW of 404.
I found out LBO or Li B O3 crystals double 808, and I found a place that can produce them. For one crystal, $2000 USD. For 100, $100 each.
Good luck with your 50mW then!

Thanks. Now it's clear.

Well, if you get intensity inside the KTP high enough, efficiency increases. But that intensity is out of your reach.

so theoretically, yes - practically, no.