Is Link Aggregation / LAG / LACP actually faster?

Simple answer:  

•  From a server to multiple clients, YES.

•  From a server to a single client, NO.

Why:  LAG/LACP does not combine several gigabit connections into a single fat connection. 

This is because all traffic for a single IP address has to go through one physical connection.  It's just too complex to do it any other way. 

So, a 4-port LAG is not a party line, where everyone can hear everyone else.  It's one person with 4 phones talking to four separate people each holding 1 phone - none of which can hear each other.

This means that a 4-port NAS can shove out 4 Gbps in total - but only 1 Gbps to each individual client.

(Yes, there are rare exceptions - just enough to make it unclear if LAG to a single client is really faster or not.  But it's not.)

This doesn't make LAG useless.  It just means it's only useful where you have several clients connecting to the NAS simultaneously.  A single client can't take advantage of the LAG, but multiple clients can.

This also applies if you connect two NAS devices together via LAG, and transfer / migrate / replicate data between them.  Each one is a single client, and so can only receive a single lane of data (1 Gbps) - not the 4 Gbps you might expect.