Were OT Jews indwelt by the Spirit?

This is a hard question to answer. Different theological traditions give different answers. It raises trickily questions of theological method. Why is it hard to answer? 

1. There's the issue of how the jargon of systematic theology maps back onto biblical usage. In systematic theology, the designations are technical terms with a uniform meaning whereas biblical usage isn't standardized.

2. Scripture often uses metaphors to depict the work of the Spirit, viz. filling, indwelling, falling upon, new birth, new creation. In order to know what that means, we must be able to translate the metaphor into a literal concept. 

3. There's also the question of whether the Bible sometimes uses different picturesque metaphors to describe the same experience. 

4. Regeneration is an essentially Johannine category. 1 Pet 1:23 and James 1:18 are apparently exceptions, but not really. In those passages, the word of God is instrumental to rebirth whereas in Johannine usage, the Spirit is instrumental in rebirth. Likewise, in Titus 3:5, rebirth is connected with the metaphor of water. 

John speaks of "purification" (1:9; cf. 3:3), but in context, that seems to be about the remission of sin rather than spiritual renewal. 

5. Conversely, sanctification is more of a Pauline category (in NT theology). In addition, Paul uses related metaphors (new creation, new man/Adam) for spiritual renewal (2 Cor 5:17; Eph 2:5,10; 4:24; Col 2:13).

Although John uses "sanctification" terminology (Jn 17:17, 19), in context it denotes something like consecration rather than sanctification in the sense of spiritual renewal. 

So this raises the question of how to collate Johannine regeneration with Pauline sanctification.  If they were both Johannine categories or Pauline categories, they might represent distinct stages, so that we could arrange them sequentially, where regeneration precedes sanctification, but since regeneration is John's preferred category for spiritual renewal while sanctification is Paul's preferred category, they may be overlapping categories. Two different metaphors that coincide or cover much of the same ground. 

6. In OT usage, "sanctity" typically denotes cultic holiness or ritual purity rather than spiritual renewal. And that carries over into the usage of Hebrews. 

7. However, the OT also refers to circumcision of the heart (Deut 30:6; Jer 6:10), which seems to be a metaphor for spiritual renewal, equivalent to Johannine regeneration and Pauline sanctification. 

8. We need to distinguish between OT Jews generally and the remnant in particular.

9. In the OT, the action of the Spirit in relation to human agents usually concerns supernatural enablement. Conferring supernatural foresight, insight, skill, or even physical strength–rather than spiritual rebirth. 

And that's paralleled in Acts, where the agency of the Spirit has reference to the charismata (e.g. revelatory dreams and visions, xenoglossy, exorcism, miraculous healing or hexing) rather than spiritual rebirth. The main difference between that kind of empowerment and OT counterparts is that it's more widely experienced among Christians than OT Jews. 

10 Finally, there's the argument from analogy. If, in the NT, certain virtues are the fruit of the Spirit (Gal 5:22-23), and OT saints exhibit the same virtues, then by parity of argument, the same effect implies the same cause. The Spirit is the source or agent of both. That seems to be equivalent to "circumcision of the heart".