Seems like you already answered your question. Yes it is possible. You can scale this to level 4 missions fine.
Though I am not sure why you would want to not use a prop mod. MWD is the only module that is going to eat your cap pool while inactive. Afterburner will be fine for pve or using a jump drive. You can always carry a mobile depot with a jump drive / Afterburner to give yourself mobility when the situation calls for it.
As far as your Edits… that is the premise. Cap battery / rechargers for cap regen. Lows for rat specific tank / reppers. If you are using a t1 battleship for level 4s then the dual rep high resist is going to be more crucial for your tank and spank idea. Use rigs to fill gaps / free slots for other utility or whatever you need.