Can I string ethernet cables?

Absolutely. This will work.

You just need to match the wiring at both ends, so T568A or T568B.

You are talking about a splice and yes your male female ending will work but keep in mind each one is a point of fail and source to add noise to the line. Make sure you keep the color codes correct and standard. Putting a splice in like that is not a proper code approved cable run so if that is an issue you might want to look at my next suggestion. Another solution would be to use the already run line as a line to pull a new longer single cable through the conduit if possible.