Welcome to the board!
I go to daily Mass in the EF and used to pray exclusively the current LotH (I started saying the LotH before I began going to Mass in the EF). It's fine most of the time. You often miss out on the connections between the Office and the Mass, and it can be very annoying when it comes to things like octaves that aren't retained in the new calendar, feast days that in the OF are moved to the Sunday, seasonal differences (Septuagesima, for example), and other more major feast days that differ. But in general it's okay and definitely do-able. Depending on your lifestyle and preferences you may also find it desirable to have that connection with the newer calendar.
Do you know Latin well or were you considering getting that new English/Latin book for the older Office or what?