Short answer, yes. If you are referring to true closing costs, and not the down payment portion or prepaids, like insurance and per diem interest, etc., and assuming the origination fee stays constant (usually 1%), then closing costs for conventional should be cheaper. However (that is a big however), FHA loans should have a lower interest rate, and they allow up to 6% of closing costs rolled into the loan vs. only 3% for conventional, and FHA down payment requirement is only 3.5% of the purchase price vs. 5% or more for conventional. Also, the FICO score requirement for FHA is only 620, whereas you need at least a 720 for conventional. One last comment, with FHA you will have to pay upfront PMI of 1.5-1.75%....but that, too, can be rolled into the loan if there is room.
Remember, closing costs, and what you need to "bring to the table" are going to be different numbers, technically speaking. What you will have to bring to the table is the total of closing costs, prepaids,like insurance, and down payment portion. FHA will let you roll up to 6% of the costs into the loan if there is room, but you must come with at least the 3.5% down payment as a minimum.)
By the way, your loan officer should have explained everything, and should also be willing to show you a comparison between FHA and Conventional.
Hope that helps.