Not really, no. I am not sure about the details but I imagine that the Alt+F2 is simply passing the commands you run to a non-interactive, non-login shell. This type of shell will not have access to aliases, as explained in man bash:

   When bash is started non-interactively, to  run  a  shell  script,  for

   example, it looks for the variable BASH_ENV in the environment, expands

   its value if it appears there, and uses the expanded value as the  name

   of  a  file to read and execute.  Bash behaves as if the following com‐

   mand were executed:

          if [ -n "$BASH_ENV" ]; then . "$BASH_ENV"; fi

   but the value of the PATH variable is not used to search for  the  file

   name.

So, you might think that you can just set BASH_ENV to point to a file containing alias definitions. Unfortunately, aliases are not available to non-interactive shells. Again from man bash:

   Aliases are not expanded when the shell is not interactive, unless  the

   expand_aliases  shell option is set using shopt (see the description of

   shopt under SHELL BUILTIN COMMANDS below).

You might think that you could add shopt -s expand_aliases to the file defined by $BASH_ENV but that won't work because that file will be read but in a different shell.

I know this is confusing. Bottom line, you can't make aliases available to the Alt+F2 dialog.

A workaround

So, since you can't do this with aliases, what you can do is do it with scripts:

sudo -H gedit /usr/bin/geditm

That will bring up a new gedit window, add these lines to it and save the file:

#!/bin/bash

gedit --display=D1

Make the script executable:

sudo chmod a+x /usr/bin/geditm

Now, you can hit Alt+F2, write geditm and that script will be launched which in turn launches gedit with the desired options.