Depends on what you mean by delivery. 
 
Most of my meat and a few sides such as Brussels's Sprouts come from Omaha Steaks, yes I do delivery.  I also have my other groceries delivered from my local store.  So, yes, again, I do delivery.
If you mean having finished dishes delivered, no I do not with the exception of a pizza now and then.  Funny thing is that my monthly grocery bill has actually dropped some since I went delivery instead of going to the store.  There three reasons that stand out to me as to why I see a lower cost.
1)  I seldom get established packages from Omaha Steaks.  I order the meat and whatever as individual items.  Most established packages are going to have small cuts such a five ounce boneless chicken breasts in a 4-pack.  Buying as an individual item I can get seven ounce breasts in a 4-pack for just a buck or two over the five ounce package.
2)  My orders from Omaha Steaks always include free stuff.  For instance my last order included four six ounce steak burger patties ( really good) and four individual serving garlic bread baguettes.  Of course such freebies are covered in the cost of other things but the four burgers I didn't directly pay for is four meals.  Also I joined their 'Gold Club' for $40.00/year USD.  So, what do I get for that $40.00?  Well they have a point system where points are gotten through purchases,  With the 'Gold Membership' the points gained are, at least double and often 3-4 times.  I can use these points as money but don't as I figured out the game.  Every month I'll get a couple of $30.00 off e Coupons.  Along with my $10.00 Military discount on every order I already get $40.00 off of every order.  I do NOT use the gained points as money off as it is either the $30.00 coupon or points.  Still I DO use these points but for free items.  Shoot, a few orders back I got an 18 ounce package of meatballs, 4-pack of apple tarts and pulled pork just by applying points.
3)  Getting devilry service from my local grocery has cut my costs a LOT.  A big aspect on this is coupons.  I am NOT a coupon clipper; never have been and never will.  When I order on-line from my grocery it automatically tells me if there is a coupon.  I just click 'apply' to use the coupon.  I also find it amazing that, in MANY cases, the on-line price is less than he price in the store.
While it would naturally differ month to month I find that my groceries cost has dropped, on an average, of $50.00-$100.00 a month.