Will I detect any signal if I apply laser light on one of the two light sensors placed in a sunlight?
Yes it should work, assuming the sensors are well matched. Allow for some leeway. Eg require the signal to reach a minimum difference between the sensors before outputting HIGH. If you give more info, eg purpose of system, what's driving /controlling the laser, and that your final output is used for, I could help with a circuit.  

You may be able to avoid needing two sensors if you encode the laser, or at least pulse it. For example, have it pulse at 1kHz (assuming your sensors react fast enough). Then filter out signals below that, then smooth that result and add a schmitt trigger for your final logic signal. This is the idea behind how IR remote control receivers block out ambient light from interfering. The underlying frequency, eg 1kHz is called the carrier frequency. 

Either way, using a light filter which blocks everything but the laser light colour could help.  

Edit: I found this circuit from here which looks near perfect:



As per my comment, just ignore the components after the final op-amp and feed into the MCU instead. Then just change a few values to change the reception frequency (currently 40kHz).