No, WinSCP cannot skip the FEAT command.
You should really upgrade your vsftpd server.

There is an issue with an FTP server for which I have no control over, where I can't successfully complete the connection sequence with WinSCP. I'm connecting with FTP in passive mode, and after turning on WinSCP logging, I see that when WinSCP sends the "FEAT" command, that is when the server connection dies. I verified this using the windows commandline ftp.exe to connect to the server, and when I executed "quote FEAT", the connection died on me.

Is it possible to somehow remove this from the connection sequence? FileZilla is able to connect because it never sends the FEAT command (according to the logs), and so the server admin won't fix the issue on his end.

Here is the log (scrubbed):
. 2014-01-17 18:32:06.322 Connecting to xxx.xxx.xxx.xxx ...
. 2014-01-17 18:32:06.326 Connected with xxx.xxx.xxx.xxx. Waiting for welcome message...
< 2014-01-17 18:32:06.462 220 (vsFTPd 2.0.1)
> 2014-01-17 18:32:06.462 USER xxxxxx
< 2014-01-17 18:32:06.547 331 Please specify the password.
> 2014-01-17 18:32:06.547 PASS ***********
< 2014-01-17 18:32:06.711 230 Login successful.
> 2014-01-17 18:32:06.711 SYST
< 2014-01-17 18:32:06.797 215 UNIX Type: L8
> 2014-01-17 18:32:06.797 FEAT
< 2014-01-17 18:32:06.881 211-Features:
. 2014-01-17 18:32:21.482 Timeout detected.
. 2014-01-17 18:32:21.482 Connection failed.
. 2014-01-17 18:32:21.482 Got reply 1004 to the command 1
* 2014-01-17 18:32:21.487 (ESshFatal) Connection failed.
* 2014-01-17 18:32:21.487 Timeout detected.
* 2014-01-17 18:32:21.487 Connection failed.
* 2014-01-17 18:32:21.487 Features: