What will be the Gain if the resistor value tends to infinity?
Yes, \$v_{\pi}\$ will still be equal to \$v_{in}\$.
For a more interesting question, consider the case where the input source is not an ideal voltage source, but a non-ideal source with a non-zero Thevenin resistance.
Now, the input voltage seen by your amplifier is the output of the divider formed by the source resistance (call it \$R_s\$) and \$r_\pi\$. Then increasing \$r_\pi\$ tends to make the input seen by the amplifier closer to the source voltage (i.e. reduces the effect of \$R_s\$). Taking \$r_\pi\to\infty\$ results in an ideal amplifier where the signal source's output resistance doesn't affect the gain.