It is very unlikely that this will work reliably.

As this is your final year, you should have come across the terms "in-band" and "out-of-band" in terms of telephone signalling?

Basically, "in-band" means that the signalling is carried in the same "channel" as the payload - in voice telephony terms, that means that the signalling will be audible in the other party's earpiece.
DTMF and call-progress tones such as Dial Tone and Busy (Engaged) Tone are examples of "in-band" signalling.

"out-of-band" means that the signalling is not carried in the same "channel" as the payload - in voice telephony terms, that means that the signalling will not be audible in the other party's earpiece.
Pulse (or "Loop-Disconnect") dialling is an example of "out-of-band" signalling: the signalling takes place between the phone and its local exchange - it is not transported across the network to the called party!
(ISDN uses "out-of-band" signalling: it has a separate channel - the D-Channel - for signalling)

Clearly, for your project to work over a standard analogue telephone line, you must use in-band signalling.

Yes, in some circumstances, it may be possible to hear some clicks due to pulse dialling from the other phone, but you should certainly not design a system that relies upon this!

DTMF has been specifically designed for this purpose - use it!