I'm not a screen expert, so there is probably a better solution, but this might be good enough for you. slowpaste only applies to the paste command, but it is possible to use xsel to copy the current X11 selection to a file, and then use screen's readreg command to read this file into a register. Finally, paste can paste a register's contents. The following in ~/.screenrc worked for me:

defslowpaste 100
bindkey ^v eval "exec |sh -c 'xsel -o >/tmp/sel </dev/null'" "readreg p /tmp/sel" "paste p"

Using slowpaste and a per-character delay in milliseconds does not seem to work in this startup file as there is no current window yet, but setting the default value with defslowpaste works well.

This binds the control-v key to a sequence of 3 commands. The exec one runs xsel -o to get the X11 selection into a file /tmp/sel, the readreg reads this file into register p, and the paste command causes the characters to appear with a delay of 100msecs between them.

I'm not a screen expert, so there is probably a better solution, but this might be good enough for you. slowpaste only applies to the paste command, but it is possible to use xsel to copy the current X11 selection to a file, and then use screen's readreg command to read this file into a register. Finally, paste can paste a register's contents. The following in ~/.screenrc worked for me:

defslowpaste 100
bindkey ^v exec sh -c 'xsel -o >/tmp/sel; screen -X eval "readreg p /tmp/sel" "paste p"'

Using slowpaste and a per-character delay in milliseconds does not seem to work in this startup file as there is no current window yet, but setting the default value with defslowpaste works well.

This binds the control-v key to a shell script of 2 commands. The first one runs xsel -o to get the X11 selection into a file /tmp/sel. The second one invokes screen with 2 builtin commands: readreg reads the file into register p, and   paste causes the characters to appear with a delay of 100msecs between them.

This uses the information from Stéphane Chazelas's answer about exec returning immediately, so you cannot use eval to chain it with other commands; the answer also explains how using the default exec "fdpat" of ... you can now replace the xsel by a cat, for example, and read input from the user upto an end-of-file control-D.