You'll want to take into consideration that all data held in the database is stored in GMT or UTC. It's only when it's returned that it's converted for display in the User's Local Time Zone. So without knowing the context in which your query will be run via Apex, I'm not certain anyone can answer your question.
If the Apex is run in a system context, you'll get one answer. If it's run in the context of a specific user, you'll get a different answer. Without telling us how you plan to execute the Apex code, no one can answer your question with any degree of certainty. If your desire is to run some kind of report by a user who's located in in the same location as where your Organization is headquartered, then you'd have something more specific that you'd be able to get results from. All you'd need to do then, is run the query from that specific location and you'd obtain the results you're looking for.
If you run the query from some other location, then you'll want to calculate the offset between that timezone and the timezone of your Org. Why? Because what's returned at that location will be returned in it's timezone, not the Org's timezone and you'll want to convert those results to the local time of your Organization. It's the offset between the two timezones that will be what's of importance to you. There's a Timezone Class that has methods that can help you with those calculations.
With that having been said, I recommend you look at Date-Time methods as there is no method called
convertTimezone (there's only
getOffset() and a few others).
The things I'm familiar with that would seem to be helpful would be
format(DateFormatString, timezone) and
formatGMT(DateFormatString, timezone). You can also
parse(Date-TimeString) to get a Date-Time in your localtimezone or use something like
valueOf(fieldValue). What you'll actually need to do will depend on your specific implementation. Be sure to look at the Date methods too as they may be appropriate as well. There are numerous ways of doing this, all of which are dependant on how you decide to implement this.