Absolutely! The problem some people see in that - for which it is NOT the fault of the truth - is it seems to be saying God doesn't care when we sin or that such a gospel is "cheap grace" or a license to sin. Of course Paul dealt with the same exact contentions in his day but it seems no matter what he said or what other Scriptures say, there will always be those who interpret it wrong. Most, of course, are those who do not understand the gospel of grace in the first place because they have been taught (or it's just human nature) that nothing is free in life. They see the greatest thing in all the world - eternal life in Heaven - as something to be earned or deserved.
We know where such false teaching comes from - the father of lies himself. Satan's very first lie to humans was, "Did God really say...?". He caused doubt and from that doubt the first humans sinned against God. They doubted God's word just as those do today who insist that eternal life can not possibly be a gift of grace. Man always has to put in his two cents. It boils down to pride - an inability to accept we cannot merit Heaven. It is SO hard to admit our impotence or to submit ourselves to mercy by first admitting we NEED it. Even Satan's sin was the sin of pride - thinking HE could be as great and good as God. That HE was somehow above all the other created beings and equal to God. How far he fell from his lofty position! But fall he did and the rest of his existence is spent in drawing as many away from God as he can. He is VERY successful especially with those who esteem their own merit and goodness and rely upon it to earn eternal life.
It is ONLY when we submit ourselves humbly before God, acknowledging our sinfulness and what we REALLY deserve that God can lift us up and seat us with Christ in the heavenlies, make us his children and indwell us with His Spirit. He who humbles himself will God lift up. We learn to walk as he would have us by submitting ourselves to His discipline, knowing that He loves us and wants what is best for us. How much is missed by those who live in fear of a judgmental, condemning God who, as you say, sits by the zot button waiting to catch us in a sin. The Holy Spirit, which God gives to those who are His, is within us for keeps - never to leave us or forsake us - as the "earnest of our inheritance". There is nothing we can do to separate us from the love of God.
For I am persuaded, that neither death, nor life, nor angels, nor principalities, nor powers, nor things present, nor things to come, nor height, nor depth, nor any other creature, shall be able to separate us from the love of God, which is in Christ Jesus our Lord. (Romans 8:38,39)
11 In him we have obtained an inheritance, having been predestined according to the purpose of him who works all things according to the counsel of his will, 12 so that we who were the first to hope in Christ might be to the praise of his glory. 13 In him you also, when you heard the word of truth, the gospel of your salvation, and believed in him, were sealed with the promised Holy Spirit, 14 who is the guarantee of our inheritance until we acquire possession of it, to the praise of his glory.
We have it NOW. The guarantee of it is the Holy Spirit in our lives. Anyone who has the Holy Spirit in them can KNOW they are saved because God doesn't lie. The Holy Spirit is our guarantee of our inheritance which we HAVE now.