Can I rollover funds from my previous 401(k) into my current account in order to maximize my annual contribution? I won't make enough through the rest of the year to max out via deductions from my remaining paychecks.

A rollover of an account is not considered a contribution - one has nothing to do with the other. The max contribution limit this year for someone under 50 years old is $15,500 - that's for new funds that you defer from this year's paychecks. When you roll funds from an old 401(k) into your current employer's plan that is not counted towards the conribution limit.