Shell – status check for sleep command

First of all, while they are functionally equivalent, $(…) is widely considered to be clearer than `…` — see this, this, and this.  Secondly, you don’t need to use $? to check whether a command succeeded or failed.  My attention was recently drawn to Section 2.9.1, Simple Commands of The Open Group Base Specifications for Shell & Utilities (Issue 7):

A "simple command" is a sequence of optional variable assignments and redirections, in any sequence, optionally followed by words and redirections, terminated by a control operator.

When a given simple command is required to be executed …
                          ⋮                                                                                (blah, blah, blah …)

If there is a command name, execution shall continue as described in Command Search and Execution.  If there is no command name, but the command contained a command substitution, the command shall complete with the exit status of the last command substitution performed.  …

For example,

• the exit status of the command

  ls -ld "module_$(uname).c"
  

  is the exit status from the ls, but

• the exit status of the command

  myfile="module_$(uname).c"
  

  is the exit status from the uname.

So ferada’s answer can be streamlined a bit:

if output=$(/etc/grub.d/30_os-prober)  &&  [ -z "$output" ]
    # i.e., if 30_os-prober successfully produced no output
then
    install_linux_only
else
    install_dual_boot
fi

Note that it is good practice to use all-upper-case names only for environment variables (or variables to be visible throughout the script).  Variables of limited scope are usually named in lower case (or, if you prefer, camelCase).