Wireless controller coupled with PS2 > Wii converter?

My question is fairly straightforward and I have searched to no avail;
I have a wireless PS2 stick, is it possible to use a PS2 > Wii converter with a wireless controller? I’d like to use my stick to play TvC on the wii without having to buy another stick.
I’m slightly worried that a wireless controller through the wireless wiimote itself will cause lag. If this scenario is even possible, is lag something that is likely?


I’d probably think the brunt of the lag would come from the conversion, not the wirelessness. But, you could always check http://shoryuken.com/f177/converter-compatibility-thread-181187/