LIPO Battery: Bare Arduino on LiPO cell charging circuit components
Short answer: yes.  I'm assuming that you're going to do input -> charger -> cell -> step-up -> circuit, and that the output current rating is adequate for your needs.

It looks like the charger is set for 500ma charge current, so check your cell can cope with that. Most mobile phone size cells can.

Do not put a bypass from the 5V input to the output of the step-up, without checking that this is OK.

There are also warnings, on the product page, about not connecting the battery backwards and that the charger gets warm in operation, both of which you should heed.