You can certainly get by with your balanced tuner, but it wouldn't be my preference. On 160 especially, the SWR can rise PRECIPITOUSLY (hmmm....I guess something can only FALL precipitously, to be grammatically correct) as you move off frequency. If you really are using a full sized L, with no loading coil, it won't be QUITE so extreme...but....any significantly shortened and loaded antenna will have a pretty high Q.
I learned a while back that 160 isn't the band you want to "get by" with....you have to "mean it" to do anything worthwhile on 160. Or, to rephrase:
"Life's too short for a lousy 160 antenna."