tl;dr
With select: no (unless in some very cumbersome way that involves more than Bash).
Analysis
This is what help select prints in Bash 5.2.37 [formatting and emphasis mine]:
select:select NAME [in WORDS ... ;] do COMMANDS; doneSelect words from a list and execute commands.
The
WORDSare expanded, generating a list of words. The set of expanded words is printed on the standard error, each preceded by a number. […] The PS3 prompt is then displayed and a line read from the standard input. If the line consists of the number corresponding to one of the displayed words, thenNAMEis set to that word. If the line is empty,WORDSand the prompt are redisplayed. If EOF is read, the command completes. Any other value read causes NAME to be set to null. […]COMMANDSare executed after each selection until abreakcommand is executed.[…]
select expects a number. What it expects does not depend on any word you pass in WORDS. Sole Enter sends an empty line. Bash states explicitly: if the line is empty, WORDS and the prompt are redisplayed.
The only way to select the 2nd (in general: Nth) line by pressing just Enter is to make Enter result in 2\n for select to read (instead of sole \n).
If Bash used Readline when handling select (which is a keyword) then this could be done by configuring Readline, I think; but it does not use Readline, it uses the line discipline. The line discipline can be configured to convert \r (generated by Enter) into \n, this is what it actually does when you run select; but there is no way to make the line discipline convert \r to 2\n.
Under tmux there is a way to make Enter result in the sequence normally sent by 2Enter:
tmux bind-key -T root Enter 'send 2; send Enter'If your script (running under tmux) called this before select (and called tmux unbind-key -T root Enter later to revert), then you would kinda achieved what you want. Still this would affect Enter for other tmux panes and tmux windows for you. I think it is possible to restrict this for a specific pane, cumbersome though, so I won't even try.
Similarly you may be able to make Enter result in the sequence normally sent by 2Enter by configuring the terminal emulator that provides a tty for the script. Doing this from within the script may or may not be easy (if possible at all), depending on which terminal emulator you use.
When using a virtual console, you probably could achieve what you want by using loadkeys and a custom file. This has its own problems.
There are probably other ways: rlwrap, expect, …
One way or another: cumbersome, requiring and affecting more than Bash that runs select.
Alternative
If you really want sole Enter to trigger a specific action, rewrite your script using read (in a loop if appropriate) instead of select. An empty line will not be special, you will be able to detect it and do whatever you want in response.