If I say yes and you bottle and things go south in a dangerous way, will you hold me liable? 3.5-4 volumes is pushing the limits. But if they are the thicker ones, give it a go. My suggestion is that if you bottle for that volume, put the case(s) of bottles in a plastic bag for the duration so just in case some blow, you won't have a huge mess.
Second ? : Carbonation is an equation with variables of time and temperature. At a higher temperature, your bottles could carb in a week. Lower temp, many weeks. Very low temp, maybe never..... If you do your sugar calculations and input correctly for 4 volumes, then eventually the yeast will eat all that sugar and fart out 4 volumes of CO2. Time and temp. Probably three weeks at about 68 would do the trick.
"Beer, well respected and rightly consumed, can be a gift of God. It is one of his mysteries, which it was his delight to conceal and the glory of kings to search out."
The Search for God and Guinness by Stephen Mansfield