Yes, at some point your delta will start approaching unity and other greeks will be close to zero. Of course, it's gonna hurt oh so much on the way there.
"An opportunity to keep things somewhat reasonable" means that you would trade delta or hedge somehow? In my experience, when the shit is already airborne, it's too late to hedge anything. In fact, any adjustments like hedging your delta in a reactive manner will hurt even more.
In a term structure (or any other spread), you are not really reducing your risk, you are replacing the outright trade with a relative value one. E.g. in case of a vertcal spread, you are trading a whole bunch of relative risks (term structure, forward vol, gamma vs vega etc). In case of a big vol move, you are probably not gonna fare well anyway, because the gamma will hurt more and the vega leg can be a total bitch during a relief rally (if you have a calendar on both vega and gamma will go against your in a relief rally).
In general, if you are converting a single leg trade into a spread purely for risk mitigation purposes, you should simply reconsider the size of the alpha leg and do it standalone.
PS. I am not saying that you should not do it, I am just saying that the best way to avoid a blow up is to (a) size your trades intelligently and (b) make sure you are selling what it makes sense to sell.