@tbeb 

While there are other factors to consider when looking to improve internet speed the short answer is, yes.   An archer T3U can connect to the 5GHz band which has a higher throughput and ability to provide higher internet speeds.  You will still need to consider network congestion, enviromental interference and distance though.  But generally speaking you will see better speeds with this upgrade.  

@tbeb 

Yes, because its is the adapter that is in use that would define the networks capablities.  If you use the USB adapter instead of the built in one you would have the ability to connect to 5GHz if that adapter supports 5Ghz which the Archer T3U does.