I think by "Can this object reach the Moon?" you are asking the wrong question. In order for something to reach a given destination the only parameters are its velocity and the distance. Even something traveling only at 1mm/s could reach the moon eventually (or any other target in that matter).
However, if you look for example at the LightSail project from the Planetary Society, they are using the momentum of the photons that are coming from the sun. This gives them a rather "low" acceleration of a few mm*s^(-2) but since they don't need any propelant (or fuel) they can accelerate basically for an infinite amount of time, allowing them to reach much higher velociities (given enough time) than rockets relaying on some kind of fuel.
This makes something like the LightSail a very good alternative to rockets when you try to reach object further away, since a rocket would need a lot of fuel, while the light sail does not need any. However, for close targets like the moon, a rocket would be much faster and probably also more ecnomic.
With a laser stationed on earth you can increase the acceleration of the satelite that has a light sail by quite a bunch and therefor make it even a more viable alternative to classic rocket propulsion. But still for close targets like the moon rockets will probably be the best tech to go for in the near future.
Note that also the Starshot project plans on using lightsails with a stationary laser station on earth to accelerate their light sails to around 20% of light speed, with that we could reach alpha centauri in around 20 years, or pluto in only around a day!