tl;dr
Yes (23andme) and no (AncestryDNA)
Long version:
As others rightfully pointed out triangulation is the key task to be performed. 23andme has it's own tool (Family Inheritance) whereas AncestryDNA has decided not to give such a tool to it's user (despite many of them complaining and explaining their wishes to have one). So with AncestryDNA you don't get the right tool nor the right data to do triangulation.
Before everyone is shouting out "That's wrong, you can move your data to GEDmatch") let me explain a bit more. Yes, you can but that still doesn't help you if your fellow possible DNA cousin on AncestryDNA isn't doing the same, right? Yes, you might be lucky and you find another two matches at GEDmatch that triangulate but that's a very minor chance (I still have a lot of segments with only one other person matching, not the required two).
As for the detailed question about mtDNA and Y-DNA the short answer is no. The long answer is that you get an estimation from 23andme which is quite good but it's based on an outdated haplotree. Yes, you can download your raw data and check it against other tools to see where in the newest tree you end up (this is how I came up with my mtDNA and Y-DNA) but keep in mind that not all SNP's are tested at 23andme or AncestryDNA.
Furthermore you can't compare it against mtDNA and Y-DNA tests from FTDNA (the only place to buy and test for both) as they are based on a different method (in case of Y-DNA that is STR - short tandem repeat) and as I said you lack the data points to compare against the Y-search and mtDNA search pool (forgot the name - can some add it as a comment?).
Hope this explains it well enough, otherwise please ask questions if points are unclear, happy to help