The answer, surprisingly, is no. Not if we correctly understand the gospel itself.
The author of the letter to the Hebrews (anonymous, parallel with many of the Old Testament books) put matters this way:
"...Since a promise remains of entering His rest, let us fear lest any of you seem to have come short of it. For indeed the gospel was preached to us as well as to them; but the word which they heard did not profit them, not being mixed with faith in those who heard. For we who have believed do enter that rest, as He has said:
'So I swore in My wrath,
"They shall not enter My rest,"'
although the works were finished from the foundation of the world. For He has spoken in a certain place of the seventh day in this way: 'And God rested on the seventh day from all His works'; and again in this place: 'They shall not enter My rest.'" (Hebrews 4:1-5)
Earlier the author quoted Psalm 95, in which the objects of wrath are the Israelites who turned back from the Land of Promise despite God's assurances that they would be victorious over apparent obstacles. They are the object lesson of God's word "not being mixed with faith"--their turning back showed their lack of trust in His promises. Faith alone makes the Bible's words truly profitable (though they are beautiful literature in their own right), both now and forever, as it opens up a relationship with the Creator of everything.
Next, the point is made that believing in God's word is entry to His rest. God is resting? Yes; the word choice in Psalm 95:11 there isn't arbitrary. The author backs up to Genesis 2:2, showing that God has finished everything He started in creation.
Do you believe that simple verse--that God is done with His work?
I'm not implying that He isn't active in the world. But He isn't laboring for anything now. When Jesus said on the cross, "It is finished [paid in full]," He wasn't kidding. In an eternal sense, the Lord's work is done, and the gospel--Christ the Creator voluntarily taking the place of sinful rebels who deserved death, paying in full their debt of punishment before God the Father on the cross--brings this idea of rest from creation into completion of His eternal plan of rescue.
So God is at rest, and trusting Him through Jesus means in some sense that we "enter that rest."
"Since therefore it remains that some must enter it, and those to whom it was first preached did not enter because of disobedience, again He designates a certain day, saying in David, 'Today,' after such a long time, as it has been said:
'Today, if you will hear His voice,
Do not harden your hearts.'
"For if Joshua had given them rest, then He would not afterward have spoken of another day. There remains therefore a rest for the people of God. For he who has entered His rest has himself also ceased from his works as God from His. Let us therefore be diligent to enter that rest, lest anyone fall according to the same example of disobedience." (Hebrews 4:6-11)
The author points out that when David wrote Psalm 95, sitting in the land of Canaan from which those faithless Israelites fled (leaving Joshua's generation that victory), he chose the present tense under the inspiration of the Holy Spirit. God through David was speaking of a rest greater than the one which Joshua accomplished in entering the Promised Land, a rest which Canaan itself foreshadowed.
If you haven't read Hebrews in full, I highly recommend taking an hour or two to do so--no need to rush. A recurring theme, seen in the phrase "remains therefore a rest," is that the promises of God are fulfilled in Jesus in a superior fashion to the lesser fulfillments of the old covenant under Moses.
This rest which is better than Joshua's means that the believer "has ceased from his work" like God. This is only possible through faith in Jesus, Who alone truly obeyed the Father while on earth. Our attempts at making ourselves impressive to God are lethally flawed--His loyalty never faltered, though we can see it tested to the uttermost in Gethsemane and upon the cross-wood.
Let us cease striving and, by faith in the completed work of Christ, be grateful to God. For from now on, anything He gives us the heart, strength and mind to do for Him is the overflow of His love for us, not the cause of it. We need not earn His approval--we labor from it. Resting at least once a week is a tangible reminder that none of our earthly efforts are ultimately required for salvation or anything else--only the free grace and provision of our heavenly Father.
That's an attitude which the world cannot produce or mimic. Walk in this freedom with me!