minimum C rate of battery cells
Assuming perfect charge efficiency, that battery needs to be supplied \$3.7V \times 10A \times 3600s = 133.2kJ\$ to charge.
At the maximum solar cell output of 0.3W and assuming all of it goes to the battery, it would take \$\frac{133.2kJ}{0.3W}=444,000 seconds = 123 hours\$
to supply that. Since that faster than it takes for the battery to self-discharge, yes it will charge. You might not want to wait around though.