How to force DistributionChart to plot empty datasets?

Update: a custom ChartElementFunction that can be combined with built-in ChartElementFunctions:

ceF2[cedf_: ChartElementDataFunction["Density"]][vpos_: {0, 0}] := If[#3 == {"empty"}, 
 {PointSize[Large], Point[Mean@Transpose@{#[[1]],vpos}]}, cedf[##]] &

Examples: using a dataset that does not require version 10 functions

SeedRandom[1]
datac = {{RandomVariate[PoissonDistribution[5], 30], 
    Labeled[{}, "Empty", Center], 
    RandomVariate[NormalDistribution[], 50]}, {{}, {}, {0, 
     0}}, {RandomVariate[PoissonDistribution[3], 50], 
    RandomChoice[{1, 2, 3, 4, 5, 6}, 100], {}}, {{1, 2}, {3, 4}, {5, 6}}};


vp0 = Min[datac /. Labeled | Style -> (#1 &)];
DistributionChart[Map[Labeled[# /. {} | Labeled[{}, __] :>
    ((vp = {vp0 - 1, vp0 - 1}) -> "empty"), 
    Length[# /. Labeled -> (# &)], Below] &, datac, {2}], 
 BaseStyle -> EdgeForm[], BarSpacing -> {.2, 1}, 
 ChartLabels -> {"s1", "s2", "s3"}, ChartStyle -> 63, 
 ChartElementFunction -> ceF2[][vp], ImageSize -> 600]

Use

ChartElementFunction -> 
 ceF2[ChartElementDataFunction["GlassQuantile", "Quantile" -> 10, 
    "QuantileShading" -> True]][vp]

to get

---

Original post:

Your data modified to have both {} and {0,0} elements as well as elements with zero mean:

datab= <|"D1" -> <|"s1" -> {1, 2, 3, 4}, "s2" -> Labeled[{}, "Empty", Center],
             "s3" -> {-3,-2,2,3}|>,
   "D2" -> <|"s1" -> {}, "s2" -> {}, "s3" -> {0,0}|>,
   "D3" -> <|"s1" -> {3, 4}, "s2" -> {1, 2, 3, 4, 5, 6}, "s3" -> {}|>,
   "D4" -> <|"s1" -> {1, 2}, "s2" -> {3, 4}, "s3" -> {5, 6}|>
   |>;

Use metadata to distinguish empty sets, and modify the ChartElementFunction to render empty sets as Points:

vp0 = Min[datab /. Labeled|Style->(#&)];
DistributionChart[Map[Labeled[#/.{}|Labeled[{},__]:>
   ((vp={vp0-1,vp0-1})->"empty"), 
   Length[# /.  Labeled ->(#&)], Below] &, datab, {2}],
 BarSpacing -> {.2, 1},ChartLabels ->{"s1", "s2" , "s3" },
ChartElementFunction -> (If[#3 == {"empty"},   
   {PointSize[Large],Point[Mean@Transpose@{#[[1]],vp}]},
   Rectangle @@ Transpose@#1] &)
]

Or define a custom ChartElementDataFunction

ceF[vpos_:{0,0}]:=If[#3 == {"empty"}, PointSize[Large], 
   Point[Mean@Transpose@{#[[1]],vpos}]}, Rectangle@@Transpose@#1] &

and use as

DistributionChart[Map[Labeled[#/.{}|Labeled[{},__]:>
   ((vp={vp0-1,vp0-1})->"empty"), 
   Length[#/.  Labeled[{},__]:>{}], Below] &, datab, {2}],
 BarSpacing -> {.2, 1}, ChartLabels ->{"s1", "s2" , "s3" },
 ChartElementFunction -> ceF[vp]
]

(* same picture *)

Would this work for you? I need to assume the data can be transformed into

xData = 
   <|"D1" -> <|"s1" -> {1, 2, 3, 4}, "s2" -> {0, 0}, "s3" -> {3, 4, 5, 6}|>, 
     "D2" -> <|"s1" -> {0, 0}, "s2" -> {0, 0}, "s3" -> {0, 0}|>, 
     "D3" -> <|"s1" -> {3, 4}, "s2" -> {1, 2, 3, 4, 5, 6}, "s3" -> {0, 0}|>, 
     "D4" -> <|"s1" -> {1, 2}, "s2" -> {3, 4}, "s3" -> {5, 6}|>|>

Then the a distribution chart that indicates zero data items where the inner associations have value {0, 0}, can be drawn with

plot = DistributionChart[
  Map[Labeled[#, If[# == {0, 0}, 0, Length @ #], Below] &, xData, {2}],
  BarSpacing -> {.2, 1},
  ChartLabels -> Automatic,
  ChartElementFunction -> ((Rectangle @@ Transpose @ #) &)]

Note: the original data can transformed in the form I use here with

xdata = data /. _Labeled -> {} /. {} -> {0, 0};