There are no differences between functions in this regard. If you installed the 64-bit version of Mathematica then it's 64-bit.
I tried this on a random graph with more than 500000 nodes and more than 600000 vertices and got a response almost immediately.
In[18]:= $Version
Out[18]= "11.3.0 for Mac OS X x86 (64-bit) (March 7, 2018)"
In[19]:= SeedRandom[42];
In[20]:= g =
With[{g = RandomGraph[{600000, 700000}]},
Subgraph[g, First@ConnectedComponents[g]]];
In[21]:= {VertexCount[g], EdgeCount[g]}
Out[21]= {520635, 687488}
In[22]:= RandomSample[VertexList[g], 2]
Out[22]= {382368, 532560}
In[23]:= GraphDistance[g, ##] & @@ %
Out[23]= 21
