mew is in an event early in the game (before misty)
and yes you can... but:
there is one small issue between version 1.0 and 1.1 .sav files...
the flags for the mystical dogs are different... so if you start with a 1.0 .sav AFTER Mt. Moon... then switch to the 1.1 rom... at some point you will walk up to a room with all 3 mystical dogs chilling in it (in rock tunnel) but when you fight them they will all be the same dog... it does not hurt furthur gameplay, you are even welcome to catch it 3 times if you really want... I reccomend NOT fighting them until you can handle a lv50 fight tho... itd suck to be killed near the end of rock tunnel (the route 2 mustical dog is not altered, you will only find 1 dog of the correct form there)
Other than that... nope no issues what so ever just change your .sav to say 1.10 instead of 1.00 or Beta
also... you will be missing out on the catch your starter option... but if you intended to pick a poke anyway (or just dont care about it that much) its not an issue, it does not alter later gameplay either.
just know that its not really a glitch if you run into a weird room with 3 dogs that all fight like 1 dog...