yeah, you can.. but you have to be really careful when enrolling in your units online. generally when you're a first year, there are no electives and there's not much choice between core units anyway; just enrol those and go to monash, get your student I.D. card.
The enrolment lady there asked me why I didn't go on the date for my course (25th jan), I told her I was going overseas and she said it was totally fine; as long as I picked all my units correctly, had photo I.D. and all my WES transaction numbers.
I picked all my core commerce/law units online, according to the handbook online, did my timetable via allocate+ and everything. I'm planning to skip the enrolment day - I called up monash if the day was COMPULSORY - apparently it's not compulsory; most people leave clueless and it's just to help orientate you a little and help you pick/units enrol.
Basically all the stuff (@ official enrolment day) - you can do them at home anyway, if you read the course handbooks.
so, yeah, I fully enrolled and got my student i.d. before actual enrolment day (I have an overseas flight at that time so yeah, can't go anyway). they then send you up to the "Airport Lounge",, assign you a host scheme buddy, walk you through awesome maccas/subway discounts of 20%, camp signup, and hand you a massive MSA calender and diary. free stuff, woot woot.
It's ok to skip the "compulsory" enrolment SESSIONS themselves as long as you make it up some other time; just call them up and ask.
remember, your enrolment is "complete" once you get your student i.d. card at monash

good luck! oh and, TrueTears is right - you can't get all the same "information" and the enrolment-day stuff if you miss the day. But the stuff isn't that important; you CAN definitely enrol earlier or after your set date though.