The relationship between oil and agricultural prices is actually somewhat more complex and ambiguous. The direction of causality is actually greater from agricultural commodities TO oil rather than the other way around, driven by fertilizer prices more than anything else. (I.e., natural gas -> fertilizer -> ag prices AND fertilizer -> oil)  Oil prices are almost always shown, empirically, to RESULT from changes in other commodity prices, contrary to the way most narratives assume happens.

Also, fuel is a significant but still not a very large part of the cost of agricultural production (less than 10% of total variable costs, if I recall).  So variation in oil price is going to be less important than the variation in the value the dollar and won't be a limiting factor regarding terms of trade.