It depends on the frame of your bike. If you have 126mm spacing (most 6-speeds) AND you have enough clearance with the chainstays (i.e. the chain won't hit your frame when moving to the lowest gear on the 7 speed, which is wider), then the 7 speed will work fine! Occasionally this requires removing a spacer from the non-freewheel side of your axle and putting it on the outside of the freewheel side of your axle. This creates a little more room on that side for the extra gear.

Your derailleur will most likely take care of the chainline, so that's not a problem! This isn't a singlespeed afterall! Geared bikes are supposed to run chainlines that are not straight.

If the 28t low gear is a bigger cog than you currently have on the bike, you may need to lengthen your chain by a few links (otherwise you will lock up the derailleur in certain gear ratios).