Will it be weathertight? It should if done properly. It is a legitimate installation method, and approved by manufacturers. Is it the BEST method? NO. Your alternatives are to R&R the siding, or to cut the siding back. IMO, R&R of the siding is pretty extreme for a house full of windows, as you are going to pay for nearly the entire house to be resided minus materials. You also deal with fade lines at seams, potential of breaking pieces, etc. What I like to do in these circumstances is to cut back the siding to allow for the full nailing fin removal and install of the new window with fin and proper flashing detail. You then add trim in the space where the siding was cut back... Full protection and weather, and it actually looks nicer IMO with trim around it, than siding up to the window frame.
Any of the three options are valid methods, each with their own pros and cons.
This is exactly my thought on the process and options as well.
Is it extra money, yes. Will it provide for a more sound and complete installation...you betcha.