Charging Li-Poly Battery with Small solar panel
I do not see any disadvantages so far. For clarification, can you explain what Li-poly IC you mean. As far as I understand you always use the same battery (Li-Poly) and it does get charged by the setup you provided.

Some improvement suggestions:

1) use Schottky diode to reduce voltage drop 
2) since you battery has integrated protection circuit, you do not need to monitor the voltage while charging. 

Notice: be careful not to esceed maximum charging current in case of too much sunlight. Typically maximum charging current is C/2 ,where C is capacity of you battery divided by hours (i.e. 10000mAH would give you C=10000mA, so C/2= 5000mA). But check your datasheet!