Yes indeed.
But the Spirit will not abide in an unclean temple.
We are the temple, and must be washed of past sin by the blood of Christ to be deemed fit for the Spirit's abode.
God's people being Spirit-filled is not exclusive to the New Covenant:Amen to that, but they could not "press into something" that was not yet provided...that being the body of Christ.
"2“See, I have called by name Bezalel son of Uri, the son of Hur, of the tribe of Judah. 3And I have filled him with the Spirit of God, with skill, ability, and knowledge in all kinds of craftsmanship, 4to design artistic works in gold, silver, and bronze, 5to cut gemstones for settings, and to carve wood, so that he may be a master of every craft." - Exodus 31:2-5
"11And it was He who gave some to be apostles, some to be prophets, some to be evangelists, and some to be pastors and teachers, 12to equip the saints for works of ministry and to build up the body of Christ
16 ...the whole body,...grows and builds itself up in love through the work of each individual part." - Ephesians 4:11,12,16
What's 'new' about the Spirit in the New Covenant is it is available to ALL of God's people, not just a select few (Kings, priests, prophets, artisans). ALL of God's people are in the ministry now, being equipped in various ways to labor with skill in the building of the temple in which God resides (us). The Day will bring to light the quality of our workmanship in the building of God:
"10 ...each one must be careful how he builds.
13 his workmanship will be evident, because the Day will bring it to light. It will be revealed with fire, and the fire will prove the quality of each man’s work. 14If what he has built survives, he will receive a reward." - 1 Corinthians 3:10,13,14