Hi,
As brought out by the posts above - the main worry is that the Initial Class I is much more detailed and thorough than a Class 2 Medical - so even if you have a valid Class 2 medical there is no guarantee that you will clear a Initial Class 1 medical. Suggest you get an Initial Class I and then pump in that large chunk of money for your training.
Once you have a valid Initial Class I, even if you do (God Forbid!) develop a problem later most Aviation Authorities would look at the possibility of giving you a waiver as they would for a medical problem in an experienced pilot.